Translate Word Phrases to Algebraic Equations
Remember, an equation has an equal sign (\(=\)) between two algebraic expressions. So if we have a sentence that tells us that two phrases are equal, we can translate it into an equation. We look for clue words that mean equals. Some words that translate to the equal sign are:
 is equal to
 is the same as
 is
 gives
 was
 will be
It may be helpful to put a box around the equals word(s) in the sentence to help you focus separately on each phrase. Then translate each phrase into an expression, and write them on each side of the equal sign.
We will practice translating word sentences into algebraic equations. Some of the sentences will be basic number facts with no variables to solve for. Some sentences will translate into equations with variables. The focus right now is just to translate the words into algebra.
Example \(\PageIndex{8}\): translate
Translate the sentence into an algebraic equation: The sum of \(6\) and \(9\) is \(15\).
Solution
The word is tells us the equal sign goes between \(9\) and \(15\).
Locate the “equals” word(s). 
The sum of 6 and 9 is 15 
Write the = sign. 
The sum of 6 and 9 = 15 
Translate the words to the left of the equals word into an algebraic expression. 
6 + 9 = _____ 
Translate the words to the right of the equals word into an algebraic expression. 
6 + 9 = 15 
Exercise \(\PageIndex{15}\)
Translate the sentence into an algebraic equation: The sum of \(7\) and \(6\) gives \(13\).
 Answer

\(7+6=13\)
Exercise \(\PageIndex{16}\)
Translate the sentence into an algebraic equation: The sum of \(8\) and \(6\) is \(14\).
 Answer

\(8+6=14\)
Example \(\PageIndex{9}\): translate
Translate the sentence into an algebraic equation: The product of \(8\) and \(7\) is \(56\).
Solution
The location of the word is tells us that the equal sign goes between \(7\) and \(56\).
Locate the “equals” word(s). 
The product of 8 and 7 is 56 
Write the = sign. 
The product of 8 and 7 = 56 
Translate the words to the left of the equals word into an algebraic expression. 
8 • 7 = _____ 
Translate the words to the right of the equals word into an algebraic expression. 
8 • 7 = 56 
Exercise \(\PageIndex{17}\)
Translate the sentence into an algebraic equation: The product of \(6\) and \(9\) is \(54\).
 Answer

\(6\cdot 9 = 54\)
Exercise \(\PageIndex{18}\)
Translate the sentence into an algebraic equation: The product of \(21\) and \(3\) gives \(63\).
 Answer

\(21\cdot 3 = 63\)
Example \(\PageIndex{10}\): translate
Translate the sentence into an algebraic equation: Twice the difference of \(x\) and \(3\) gives \(18\).
Solution
Locate the “equals” word(s). 

Recognize the key words: twice; difference of … and … 
Twice means two times. 
Translate. 

Exercise \(\PageIndex{19}\)
Translate the given sentence into an algebraic equation: Twice the difference of \(x\) and \(5\) gives \(30\).
 Answer

\(2(x5)=30\)
Exercise \(\PageIndex{20}\)
Translate the given sentence into an algebraic equation: Twice the difference of \(y\) and \(4\) gives \(16\).
 Answer

\(2(y4)=16\)
Practice Makes Perfect
Determine Whether a Number is a Solution of an Equation
In the following exercises, determine whether each given value is a solution to the equation.
 x + 13 = 21
 x = 8
 x = 34
 y + 18 = 25
 y = 7
 y = 43
 m − 4 = 13
 m = 9
 m = 17
 n − 9 = 6
 n = 3
 n = 15
 3p + 6 = 15
 p = 3
 p = 7
 8q + 4 = 20
 q = 2
 q = 3
 18d − 9 = 27
 d = 1
 d = 2
 24 f − 12 = 60
 f = 2
 f = 3
 8u − 4 = 4u + 40
 u = 3
 u = 11
 7v − 3 = 4v + 36
 v = 3
 v = 11
 20h − 5 = 15h + 35
 h = 6
 h = 8
 18k − 3 = 12k + 33
 k = 1
 k = 6
Solve Equations using the Subtraction Property of Equality
In the following exercises, solve each equation using the subtraction property of equality.
 a + 2 = 18
 b + 5 = 13
 p + 18 = 23
 q + 14 = 31
 r + 76 = 100
 s + 62 = 95
 16 = x + 9
 17 = y + 6
 93 = p + 24
 116 = q + 79
 465 = d + 398
 932 = c + 641
Solve Equations using the Addition Property of Equality
In the following exercises, solve each equation using the addition property of equality.
 y − 3 = 19
 x − 4 = 12
 u − 6 = 24
 v − 7 = 35
 f − 55 = 123
 g − 39 = 117
 19 = n − 13
 18 = m − 15
 10 = p − 38
 18 = q − 72
 268 = y − 199
 204 = z − 149
Translate Word Phrase to Algebraic Equations
In the following exercises, translate the given sentence into an algebraic equation.
 The sum of 8 and 9 is equal to 17.
 The sum of 7 and 9 is equal to 16.
 The difference of 23 and 19 is equal to 4.
 The difference of 29 and 12 is equal to 17.
 The product of 3 and 9 is equal to 27.
 The product of 6 and 8 is equal to 48.
 The quotient of 54 and 6 is equal to 9.
 The quotient of 42 and 7 is equal to 6.
 Twice the difference of n and 10 gives 52.
 Twice the difference of m and 14 gives 64.
 The sum of three times y and 10 is 100.
 The sum of eight times x and 4 is 68.
Translate to an Equation and Solve
In the following exercises, translate the given sentence into an algebraic equation and then solve it.
 Five more than p is equal to 21.
 Nine more than q is equal to 40.
 The sum of r and 18 is 73.
 The sum of s and 13 is 68.
 The difference of d and 30 is equal to 52.
 The difference of c and 25 is equal to 75.
 12 less than u is 89.
 19 less than w is 56.
 325 less than c gives 799.
 299 less than d gives 850.
Self Check
(a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
(b) What does this checklist tell you about your mastery of this section? What steps will you take to improve?