Chapter 9.1, Problem 42CCR

To determine

To solve: The given equation and check its solution.

Answer to Problem 42CCR

The solution of the given equation is $-3$ .

Explanation of Solution

Given information:

The following equation:

  $3x+2=-x-10$

Calculation:

The equation can be solved as follows:

  $\begin{array}{l}3x+2=-x-10[\text{Write the equation]}\\ 3x+2+x=-x-10+x[\text{Addition property of equations]}\\ 4x+2=-10[\text{Simplify]}\\ 4x+2-2=-10-2[\text{Subtraction property of equations]}\\ 4x=-12[\text{Simplify]}\\ \frac{4x}{4}=-\frac{12}{4}[\text{Division property of equations]}\\ x=-3[\text{Simplify]}\end{array}$

The solution is verified as follows:

  $\begin{array}{l}3x+2=-x-10[\text{Write the equation]}\\ 3(-3)+2=-(-3)-10\text{[Replace }x\text{ with }-3]\\ -9+2=3-10[\text{Multiply]}\\ -7=-7[\text{Simplify]}\end{array}$

Since both sides of the equation are equal, the solution is correct.