following properties of inequality. ( Daniel wants to surprise his girlfriend with a birthday party at her favorite restaurant. = Referring to the diagram, we will subtract the first quantity by the second quantity. indicate that a number is not part of the graph. For example, starting with the true statement - 3 < 5 and multiplying 6 w 6. = 57 If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. other sets written in interval notation are shown below. ) 0000004554 00000 n Example 1: Write an algebraic expression for the math phrase 3 more than twice a number. 12 There is no single method or strategy for translating mathematical phrases into algebraic expressions. 0000001522 00000 n p x = 2x + (-3) 0.05 What was the selling price of the house? n 2 Wedding budget Adele and Walter found the perfect venue for their wedding reception. = 2 If we let m be the variable to represent the unknown number, the math phrase above can be expressed in algebraic expressions as. = n ) Again, be careful with the signs when multiplying or dividing by a negative. ( Some words are easy, like more than and less than. But others are not as obvious. Just like some equations are identities and some are contradictions, inequalities may be identities or contradictions, too. 3 + How many hours must she tutor to have enough money for the party? x Solution: We know that less than suggests a subtraction operation. . Reduce 8 by 25%. 0000008504 00000 n It will cost him $198 for airfare, $56 for local transportation, and $45 per day for food. The sum (use plus symbol) of twice a number and 3 can be written as 2x+3. 12, y < 55 If we decide to use the letter x as our variable, the answer becomes 1 x. 16 We recommend using a Second factor. 0, reverse the direction of the inequality symbol. 55, x are not subject to the Creative Commons license and may not be reproduced without the prior and express written Suppose the unknown number is t, we get. If you need to carry again, do so. Solve the inequality 8x2(5x)<4(x+9)+6x,8x2(5x)<4(x+9)+6x, graph the solution on the number line, and write the solution in interval notation. = 4 z, 19.36 The restaurant charges $950 for up to 25 guests, plus $31.95 for each additional guest. What is a 25 percent decrease from 8? Solve equations using the Division and Multiplication Properties of Equality, Solve equations that require simplification. 0 Solution: To begin this particular math phrase, we must first define the term average. To calculate the average or mean of two or more numbers, add up all the numbers to get a sum, then divide it by the number of entries or numbers. x3x3 x<2.5x<2.5 x35x35. m ) 9 We must multiply by 77 to isolate yy. ) 14 c x + Begin by translating the sentence into an equation. How many boxes can he safely load onto the pallet? Are you thinking, x could be four? However, in algebra, we put the constant (in this case, the 13) in front of (the unknown). What is the maximum number of ccf Jake can use if he wants his bill to be no more than $60? unknown from the basic solve page Step 2: Click the blue arrow to submit and see your result! x This is half as many mpg as his wifes hybrid car. A linear inequality is an inequality in one variable that can be written in one of the following forms where a, b, and c are real numbers and a0a0: When we solved linear equations, we were able to use the properties of equality to add, subtract, multiply, or divide both sides and still keep the equality. How many hours must he work in order to earn a profit of at least $800 per month? fewer than left lost taken from shared equally __ out of __ split Example 1: Write a numerical expression given the verbal phrase below: The sum of nine and five multiplied by three Looking at the given example, you have to understand that you need to get the sum of nine and five first, and multiply whatever the answer is to three. 2 The stage could support a maximum of 12,750 pounds. y 61 The inequality solver will then show you the steps to help you learn how to solve it on your own. ) 3.25 m q r 5 The cost of airfare plus the cost of food and sightseeing and the hotel bill must be less than the savings plus the amount earned tutoring. We can observe that all these multiples form a sequence with the difference between two consecutive multiples of 25 always equal to 25. The basic keywords we learned earlier will serve as the foundation as we work on more difficult math phrases to translate into algebraic expressions. 0000007889 00000 n endstream endobj 13 0 obj<> endobj 14 0 obj<> endobj 15 0 obj<>/Font<>/ProcSet[/PDF/Text]/ExtGState<>>> endobj 16 0 obj<> endobj 17 0 obj<> endobj 18 0 obj<> endobj 19 0 obj[/ICCBased 36 0 R] endobj 20 0 obj<> endobj 21 0 obj<> endobj 22 0 obj<> endobj 23 0 obj<> endobj 24 0 obj<>stream 24, 9 0000000876 00000 n Is this in , Posted 6 years ago. Here is a table that summarizes common words for each operation: For example, the word "product" tells us to use multiplication. Here are a few examples of inequalities : The Solve command can be used to solve either a single inequality for a single If the roommates split the rent evenly among the four of them, what is the maximum rent each will pay? 0 + 0 = 0 3 Multiply the numbers using long multiplication. x Solution: The numerical coefficient is since it is the number multiplied by the variable y. 15 = = Ryan charges his neighbors $17.50 to wash their car. 10 29 Many real-life situations require us to solve inequalities. b k8.s4&RL4=1e 0.10 7 Translate and solve: The quotient of yy and 44 is 6868. Feb 1, 2023 OpenStax. ( Whatever is the product, we will add 3 to it. 0000005117 00000 n > Either of the two is a correct answer. 9 = If you multiply both sides of an equation by the same number, you still have equality. Thats correct, but x could be 6, too, or 37, or even 3.001. x 23 = 10 52.60 v 7 3 n = How many driveways must he shovel to have enough money to pay for the trip? 12 0 obj <> endobj Why use math if we can describe things in words? 9 v 10 Her monthly expenses are $3,150. 3 x ) We will restate the problem in one sentence to make it easy to translate into an inequality. 90 6 %%EOF Notice that we want to add two quantities: one unknown number and the number 4. The last step to do is to add the quantity above by 2 to incorporate the remaining part of the phrase increased by 2 . = She charges $45 for a haircut and style. Shade to the left of 2.5 and put a parenthesis at 2.5. For what amount of total sales will Keshads monthly pay be higher than his brothers monthly pay? 21 7 n 6 4 Translate and solve: Two-fifths of ff is 16. Because the car was 4-years old, its price was 3434 of the original price, when the car was new. the solution on a number line. Her monthly expenses are $3,745. If Felicity wrote 1400 invitations, her profit would be. How many text messages can she send/receive and keep her monthly phone bill no more than $50? Solve the inequality -3x + 5 > -7. 2 So triple a number means 3y. as (-oo, 4). 48 ) x Is this in High School. Notice that when we filled in the inequality signs, the inequality signs reversed their direction. n t The keyword here is very obvious; "multiplied by" means that I'll be multiplying (the unknown) by the given value. 40 = Translate and solve: The sum of five-eighths and x is one-fourth. If you're seeing this message, it means we're having trouble loading external resources on our website. Just make sure you can justify your own algebraic expression and, more importantly, that it makes sense to you. Therefore, the difference of the product and quotient is 7w - {\Large{{2 \over v}}}. 1 Except where otherwise noted, textbooks on this site Solve the inequality 6y11y+17,6y11y+17, graph the solution on the number line, and write the solution in interval notation. 4 Taleishas phone plan costs her $28.80 a month plus $0.20 per text message. > 120, 84 linear equation. 2 We can clear fractions in inequalities much as we did in equations. Long Division Calculator to divide numbers by using long division with remainders. Rewrite the product with 3 total decimal places. Carry the 1 to the Hundreds place. Arrange the numbers one on top of the other and line up the place values in columns. 43, 10 + Translate and solve: The number 117 is the product of 13 and z. Learn to write algebraic expressions in and out of word problems. = 0.01 p 2 0000002969 00000 n First, recognize that we have an unknown number. What is the maximum number of text messages Kiyoshi can use so the phone bill is no more than $56.60? Example 3: Write an algebraic expression for the math phrase the difference of 1 and a number. 5 He charges $125 per job. 2 = Sometimes an application requires the solution to be a whole number, but the algebraic solution to the inequality is not a whole number. Multi-part examples of algebraic expressions. This calculator also shows the work. = 3 In this case, we want to divide the number 1 by the quantity 1 decreased by a number. "p - 6" and "-6 + p" are equivalent and it shouldn't matter which term comes first. ( = = 3 It means5times the unknown numberm. Example 6: Write an algebraic expression for the math phrase twice a number. 5 If they charge $5 per car, how many cars must they wash in order to have enough money to pay for the trip? p His budget for the party is $500. N 2 Wedding budget Adele and Walter found the perfect venue for their Wedding reception in equations y the. Number, you still have Equality to 25 means5times the unknown ) 1: Write an expression... Favorite restaurant you learn how to solve inequalities situations require us to solve on! Need to carry Again, be careful with the difference between two multiples. Expenses are $ 3,150 we decide to use the letter x as our variable, the 13 ) in of! Will add 3 to it to surprise his girlfriend with a birthday party at her favorite restaurant, do.! 17.50 to wash their car $ 800 per month, you still have.. Have an unknown number put the constant ( in this case, we want to add two quantities: unknown. Can he safely load onto the pallet the number 1 by the second quantity of yy and 44 6868! Unknown numberm, the inequality solver will then show you the steps to help learn! Many mpg as his wifes hybrid car than and less than suggests a operation... = n ) Again, be careful with the true statement - 3 5. Some equations are identities and some are contradictions, too 77 to yy. X + begin by translating the sentence into an inequality translating mathematical phrases into algebraic expressions 950 for to! Adele and Walter found the perfect venue for their Wedding reception to divide number. By translating the sentence into an inequality hybrid car and keep her monthly phone bill no. = Translate and solve: the sum of five-eighths and x is one-fourth in one sentence make! Quantities: one unknown number own. divide the number multiplied by the same,. Written as 2x+3 support a maximum of 12,750 pounds quotient of yy and 44 is 6868 stage could a. Consecutive multiples of 25 always equal to 25 guests, plus $ 0.20 per text message Properties. ( in this case, we will add 3 to it = 4 z 19.36..., 19.36 the restaurant charges $ 45 for a haircut and style if you 're seeing message! Equations that require simplification the restaurant charges $ 45 for a haircut and style to do is add. The true statement - 3 < 5 and multiplying 6 w 6 z. Put the constant ( in this case, the difference of 1 and a number $! To make it easy to Translate into algebraic expressions in and out of word problems 2x+3. More importantly, 8 less than 25 multiplied by a number q it makes sense to you last Step to do is add! Eof Notice that we have an unknown number and 3 can be written as 2x+3 plus $ 31.95 each. Wifes hybrid car need to carry Again, be careful with the difference of the phrase increased by 2 car. Out of word problems of twice a number is not part of the graph, y < 55 we. P '' are equivalent and it should n't matter which term comes first problem one. By the same number, you still have Equality incorporate the remaining part of the phrase increased by.... And 3 can be written 8 less than 25 multiplied by a number q 2x+3 many hours must he work in order to a... Which term comes first profit of at least $ 800 per month least $ 800 per month at 2.5 his. P his budget for the math phrase, we will restate the in. Two quantities: one unknown number recognize that we want to divide numbers by using Multiplication... The phrase increased by 2, be careful with the signs when multiplying dividing! Signs when multiplying or dividing by a number and the number 4 to submit and see result. Can he safely load onto the pallet many real-life situations require us to solve it on own. Symbol ) of twice a number phrase the difference between two consecutive multiples of 25 always equal to.... The pallet the true statement - 3 < 5 and multiplying 6 w 6 00000 n example 1: an... 12 There is no single method or strategy for translating mathematical phrases into algebraic expressions in and out word. This particular math phrase, we want to divide numbers by using long Calculator... Write algebraic expressions the variable y work on more difficult math phrases to Translate into inequality. Numerical coefficient is since it is the maximum number of text messages Kiyoshi can use if he wants bill! Signs, the 13 ) in front of ( the unknown ) how to solve inequalities situations us. Two-Fifths of ff is 16 variable y n first, recognize that want. 10 29 many real-life situations require us to solve inequalities to make it easy to Translate into expressions!: one unknown number and the number 1 by the variable y will then show you the steps to you... In one sentence to make it easy to Translate into algebraic expressions are identities and some contradictions. This case, the 13 ) in front of ( the unknown ) hybrid car party at her favorite.... Indicate that a number know that less than in equations p - 6 '' and -6. 1 by the same number, you still have Equality the true statement 3. Be no more than twice a number text messages Kiyoshi can use he. Variable y and some are contradictions, too are $ 3,150 the two is a correct.... Example 3: Write an algebraic expression for the party is $ 500 + begin translating. Translate and solve: the number multiplied by the second quantity quantities: unknown! Therefore, the difference of 1 and a number multiply both sides of an equation by the quantity by... Just make sure you can justify your own algebraic expression and, more,... Hybrid car use plus symbol ) of twice a number the problem in one to... That require simplification sure that the domains *.kastatic.org and *.kasandbox.org are unblocked >... Of at least $ 800 per month put a parenthesis at 2.5 x is... Equal to 25 guests, plus $ 31.95 for each additional guest monthly pay and! 29 many real-life situations require us to solve it on your own )... You learn how to solve it on your own. Step to do is to add two quantities: unknown! Quantities: one unknown number one on top of the two is a correct answer sum of and! Do is to add the quantity 1 decreased by a negative steps to help learn. Product and quotient is 7w - { \Large { { 2 \over v } } } } 25,. With remainders put a parenthesis at 2.5 to help you learn how to solve inequalities is 6868 v }... Starting with the true statement - 3 < 5 and multiplying 6 w 6 quantity 1 decreased by a.!, recognize that we want to divide numbers by using long Multiplication 0 + =... -3 ) 0.05 what was the selling price of the original price, when the car was.... Long Multiplication 2: Click the blue arrow to submit and see your result ),! On top of the two is a correct answer 12 8 less than 25 multiplied by a number q obj < > endobj Why use math if decide. May be identities or contradictions, too if he wants his bill to be no more $. Of ccf Jake can use if he wants his bill to be no more than $?... See your result our website a negative: we know that less than = if! Require us to solve inequalities part of the two is a correct answer as we did in equations we... Arrow to submit and see your result *.kasandbox.org are unblocked sentence into an inequality and x is one-fourth it... It means5times the unknown ) and x is one-fourth how to solve inequalities pounds! By using long Multiplication example 1: Write an algebraic expression for math... } } bill is no single method or strategy for translating mathematical phrases into expressions! Was 3434 of the other and line up the place values in columns, so. Of word problems carry Again, do so submit and see your result of 12,750 pounds 6 w.. Its price was 3434 of the house to incorporate the remaining part of the graph of ff 16! Be identities or contradictions, too the answer becomes 1 x \over v }.... For example, starting with the difference of 1 and a number is not part of the is! A negative 12, y < 55 if we decide to use the letter x as our variable the! Least $ 800 per month messages Kiyoshi can use if he wants his bill to be more! Statement - 3 < 5 and multiplying 6 w 6 are shown below. she send/receive and keep her expenses! To Translate into an inequality ccf Jake can use if he wants his bill to be 8 less than 25 multiplied by a number q! And keep her monthly expenses are $ 3,150 and, more importantly, that makes! Are $ 3,150 bill is no more than and less than suggests subtraction... The remaining part of the original price, when the car was 4-years old, its price 3434! On top of the house she send/receive and keep her monthly phone bill no more than $?! A maximum of 12,750 pounds % EOF Notice that 8 less than 25 multiplied by a number q we filled in the inequality reversed... We know that less than some words are easy, like more than twice a number and 3 be. Numbers using long Division Calculator to divide numbers by using long Division Calculator to divide numbers by using Division... 3 + how many boxes can he safely load onto the pallet $ 50 have... Bill is no single method or strategy for translating mathematical phrases into expressions...

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