Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.2 Linear Equations in One Variable and Proportions - Exercise Set 6.2: 41

Answer

x = 1

Work Step by Step

The equation in the problem is given below. 6 = -4(1 - x) + 3(x + 1) To start, we will use the distributive property to distribute the -4 across the first set of parentheses and the 3 across the second set of parentheses. 6 = -4 + 4x +3x + 3 Second, we will rearrange the right side of the equation so that like terms are grouped together. Remember, the sign to the left of a term stays with the term. 6 = 4x + 3x - 4 + 3 Now, we can combine like terms on the right side of the equation. 6 = 7x - 1 Now that we have each side simplified, we can isolate the term with the variable on one side of the equation. Since it is already on the right side, let's leave it there. We can add 1 to both sides of the equation. 6 + 1 = 7x - 1 + 1 This gives us: 7 = 7x We can now divide both sides by 7. This will give us a value for x. $\frac{7}{7}$ = $\frac{7x}{7}$ By completing the division, we get x = 1. Checking, we substitute x = 1 into the original equation. 6 = -4(1 - x) + 3(x + 1) 6 = -4(1 - 1) + 3(1 + 1) Now, we perform the operations inside the parentheses. 6 = -4(0) +3(2) Then multiply/divide left to right. (We only have multiplication) 6 = 0 + 6 Last, add/subtract left to right. (We only have addition) 6 = 6 Since our numbers are equal, we have found that x = 1 is the solution to our equation.
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