Chapter 2.4, Problem 15P

Solve each equation. Check your answer.

$3w-6+2w=-2+w$

To determine

To find : the equation .

Answer to Problem 15P

  $w=1$

Explanation of Solution

Given equation: $3w-6+2w=-2+w$

Calculation:

Given equation can be written as

  $\begin{array}{l}3w-6+2w=-2+w\\ 5w-6=-2+w\end{array}$

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

  $\begin{array}{l}5w-6-w=-2+w-w\\ 4w-6=-2\end{array}$

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

  $\begin{array}{l}4w-6+6=-2+6\\ 4w=4\end{array}$

Dividing both sides of the equation by 25, we get

  $\begin{array}{l}w=\frac{4}{4}\\ w=1\end{array}$

Thus, solution of given equation is

  $w=1$

VERIFICATION:

To check that w= 1 is solution of the equation, we substitute w= 1 in both sides of equation.

  $\begin{array}{l}LHS=3w-6+2w=3\times 1-6+2\times 1=3-6+2=-1\\ RHS=-2+w=-2+1=-1\end{array}$

Since, $LHS=RHS$

Hence, solution is correct.