Chapter 2.4, Problem 13P

Solve each equation. Check your answer:

$-(5a+6)=2(3a+8)$

To determine

To find: the equation .

Answer to Problem 13P

  $a=-2$

Explanation of Solution

Given equation: $-\left(5a+6\right)=2\left(3a+8\right)$

Calculation:

Given equation can be simplifies as

  $\begin{array}{l}-\left(5a+6\right)=2\left(3a+8\right)\\ -5a-6=6a+16\end{array}$

By subtracting 6a both sides of the equation, we get

  $\begin{array}{l}-5a-6-6a=6a+16-6a\\ -11a-6=16\end{array}$

By adding 6 to both sides of the equation, we get

  $\begin{array}{l}-11a-6+6=16+6\\ -11a=22\end{array}$

Dividing both sides of the equation by -11, we get

  $\begin{array}{l}a=\frac{22}{-11}\\ a=-2\end{array}$

Thus, solution of given equation is

  $a=-2$

VERIFICATION:

To check that a=- 2 is solution of the equation, we substitute a=- 2in both sides of equation.

  $\begin{array}{l}LHS=-\left(5a+6\right)=-\left(5\times \left(-2\right)+6\right)=-\left(-10+6\right)=4\\ RHS=2\left(3a+8\right)=2\left(3\times \left(-2\right)+8\right)=2\left(-6+8\right)=2\left(2\right)=4\end{array}$

Since, $LHS=RHS$

Hence, solution is correct.