108 Chapter 2 Linear Equations and Inequalities 4. Translations We have already practiced writing an English sentence as a mathematical equation. Recall from Section 1.3 that several key words translate to the algebraic operations of addition, subtraction, multiplication, and division. Translating to a Linear Equation Example 8 Write an algebraic equation to represent each English sentence. Then solve the equation. a. The quotient of a number and 4 is 6. b. The product of a number and 4 is 6. c. Negative twelve is equal to the sum of 5 and a number. d. The value 1.4 subtracted from a number is 5.7. Solution: For each case we will let x represent the unknown number. a. The quotient of a number and 4 is 6. Multiply both sides by 4. Check: ✔ True 4 1 x 4 The number is 24. b. The product of a number and 4 is 6. Divide both sides by 4. Check: ✔ True 4x 6 3 2 The number is . c. Negative twelve is equal to the sum of and a number. Add 5 to both sides. Check: ✔ True 12 5 x 12 5 5 5 x 7 x 12 5 172 The number is 7. 5 3 2 4 a 3 2 x b 6 4x 4 6 4 24 4 x 24 6 x 4 4 6 4 x 4 4 6 6
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