Chapter 1.3, Problem 13E

To determine

To solve and check: the given equation.

Answer to Problem 13E

The required solution is $x=-3$

Explanation of Solution

Given:

  $\frac{2}{3}(3x+9)=-2(2x+6)$

Calculation:

Solve:

  $\frac{2}{3}(3x+9)=-2(2x+6)$

Given

  $2x+6=-4x-12$  Use Distributive Property

  $2x+6-6=-4x-12-6$  Subtract both sides by 6

  $2x+4x=-4x+4x-18$  Add both sides by 4x

  $\frac{6x}{6}=\frac{-18}{6}$  Divide both sides by 6

  $x=-3$  Simplify

Check:

  $\frac{2}{3}(3x+9)=-2(2x+6)$  Given

  $\frac{2}{3}(3(3)+9)=-2(2(-3)+6)$  Substitute

  $\frac{2}{3}(-9+9)=-2(-6+6)$  Simplify

  $\frac{2}{3}(0)=-2(0)$  Simplify

  $0\stackrel{\underset{\_}{r}}{=0}$  Simplify

  $x=-3$

Conclusion:

Therefore, $x=-3$