Chapter 1.2, Problem 65E

To determine

whether the given x values is a solution of the given equation or not

Answer to Problem 65E

Here, $x=-1$ is a solution but $x=2$ is not a solution.

Explanation of Solution

Given:

  $-2\left(x-1\right)=1-3x$

Calculation:

Check if $x=-1$ a solution is:

  $\begin{array}{l}-2\left(-1-1\right)\stackrel{?}{=}1-3\left(-1\right)\text{ Substitute }x=-1\text{ into the equation}\\ -2\left(-2\right)\stackrel{?}{=}1-3\left(-1\right)\text{ Simplify}\text{.}\\ 4\stackrel{?}{=}1+3\text{ Multiply}\text{.}\\ 4=4\text{ Simplify}\text{.}\end{array}$

  $x=-1$ isa solution.

Check if $x=2$ a solution is:

  $\begin{array}{l}-2\left(2-1\right)\stackrel{?}{=}1-3\left(2\right)\text{ Substitute }x=2\text{ into the equation}\\ -2\left(1\right)\stackrel{?}{=}1-3\left(2\right)\text{ Simplify}\text{.}\\ -2\stackrel{?}{=}1-6\text{ Multiply}\text{.}\\ -2\ne -5\text{ Simplify}\text{.}\end{array}$

  $x=2$ isnot a solution.

Conclusion:

Therefore, $x=-1$ isa solution but $x=2$ is nota solution.