Chapter 2.4, Problem 8P

Solve each equation. Check your answer.

$15m+22=-7m+18$

To determine

To solve: the equation .

Answer to Problem 8P

  $m=-\frac{2}{11}$

Explanation of Solution

Given equation: $15m+22=-7m+18$

By adding 7m to both sides of the equation, we get

$\begin{array}{l}15m+22+7m=-7m+18+7m\\ 22m+22=18\end{array}$

By subtracting 22 from both sides of the equation, we get

$\begin{array}{l}22m+22-22=18-22\\ 22m=-4\end{array}$

Dividing both sides of the equation by 22, we get

$\begin{array}{l}m=-\frac{4}{22}\\ m=-\frac{2}{11}\end{array}$

Thus, solution of given equation is

$m=-\frac{2}{11}$

VERIFICATION:

To check that $m=-\frac{2}{11}$is solution of the equation, we substitute $m=-\frac{2}{11}$ in both sides of equation.

$\begin{array}{l}LHS=15m+22=15\times \left(-\frac{2}{11}\right)+22=-\frac{30}{11}+22=\frac{212}{11}\\ RHS=-7m+18=-7\times \left(-\frac{2}{11}\right)+18=\frac{14}{11}+18=\frac{212}{11}\end{array}$

Since, $LHS=RHS$

Hence, solution is correct.