148 Chapter 2 Linear Equations and Inequalities Translating to a Linear Equation Forty less than five times a number is fifty-two less than the number. Find the number. Solution: Step 1: Read the problem. Let x represent the unknown number. Step 2: Label the unknown. Step 4: Write an equation. Step 5: Solve the equation. a 5 times b 1402 the a number a b 1522 number 5x 40 x 52 5x 40 x 52 5x x 40 x x 52 4x 40 52 4x 40 40 52 40 4x 12 4x 4 12 4 The number is Step 6: Write the final answer in words. Translating to a Linear Equation 3. Twice the sum of a number and six is two more than three times the number. Find the number. Solution: Step 1: Read the problem. Let x represent the unknown number. Step 2: Label the unknown. twice the sum is 2 more than Step 3: Write a verbal model. Step 4: Write an equation. 2 1x 62 3x 2 three times a number Example 3 x 3 Example 2 Step 3: Write a verbal model. Skill Practice 2. Thirteen more than twice a number is 5 more than the number. Find the number. Classroom Example: p. 154, Exercise 14 Avoiding Mistakes It is important to remember that subtraction is not a commutative operation. Therefore, the order in which two real numbers are subtracted affects the outcome. The expression “forty less than five times a number” must be translated 5x 40 1not 40 5x2 as: . Similarly, “fifty-two less than the number” must be translated as: x 52 1not 52 x2. Skill Practice 3. Three times the sum of a number and eight is 4 more than the number. Find the number. Classroom Example: p. 154, Exercise 18 less is less Answers 2. The number is 8 . 3. The number is 10.
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