example
Determine whether each of the following is a solution of [latex]2x - 5=-13\text{:}[/latex]
1. [latex]x=4[/latex]
2. [latex]x=-4[/latex]
3. [latex]x=-9[/latex].
Solution
| 1. Substitute [latex]4[/latex] for x in the equation to determine if it is true. |
|
| Substitute [latex]\color{red}{4}[/latex] for x. |
[latex]2x--5=--13[/latex] |
|
[latex]2(\color{red}{4})--5=--13[/latex] |
| Multiply. |
[latex]8--5=--13[/latex] |
| Subtract. |
[latex]3=--13[/latex] |
Since [latex]x=4[/latex] does not result in a true equation, [latex]4[/latex] is not a solution to the equation.
| 2. Substitute [latex]−4[/latex] for x in the equation to determine if it is true. |
|
| Substitute [latex]\color{red}{--4}[/latex] for x. |
[latex]2x--5=--13[/latex] |
| Multiply. |
[latex]--8--5=--13[/latex] |
| Subtract. |
[latex]--13=--13[/latex] |
Since [latex]x=-4[/latex] results in a true equation, [latex]-4[/latex] is a solution to the equation.
| 3. Substitute [latex]−9[/latex] for x in the equation to determine if it is true. |
|
|
[latex]2x--5=--13[/latex] |
| Substitute [latex]−9[/latex] for x. |
[latex]2(\color{red}{--9})--5=--13[/latex] |
| Multiply. |
[latex]--18--5=--13[/latex] |
| Subtract. |
[latex]--23=--13[/latex] |
Since [latex]x=-9[/latex] does not result in a true equation, [latex]-9[/latex] is not a solution to the equation.
