Example
Solve: [latex]8x+9x - 5x=-3+15[/latex]
Solution:
First, we need to simplify both sides of the equation as much as possible
Start by combining like terms to simplify each side.
| [latex]8x+9x-5x=-3+15[/latex] |
| Combine like terms. | [latex]12x=12[/latex] |
| Divide both sides by 12 to isolate x. | [latex]\Large\frac{12x}{\color{red}{12}}\normalsize =\Large\frac{12}{\color{red}{12}}[/latex] |
| Simplify. | [latex]x=1[/latex] |
| Check your answer. Let [latex]x=1[/latex] | |
| [latex]8x+9x-5x=-3+15[/latex] | |
| [latex]8\cdot\color{red}{1}+9\cdot\color{red}{1}-5\cdot\color{red}{1}\stackrel{\text{?}}{=}-3+15[/latex] | |
| [latex]8+9-5\stackrel{\text{?}}{=}-3+15[/latex] | |
| [latex]12=12\quad\checkmark[/latex] | |
example
Solve: [latex]11 - 20=17y - 8y - 6y[/latex]
Answer:
Solution:
Simplify each side by combining like terms.
| [latex]11-20=17y-8y-6y[/latex] |
| Simplify each side. | [latex]-9=3y[/latex] |
| Divide both sides by 3 to isolate y. | [latex]\Large\frac{-9}{\color{red}{3}}\normalsize =\Large\frac{3y}{\color{red}{3}}[/latex] |
| Simplify. | [latex]-3=y[/latex] |
| Check your answer. Let [latex]y=-3[/latex] | |
| [latex]11-20=17y-8y-6y[/latex] | |
| [latex]11-20\stackrel{\text{?}}{=}17(
\color{red}{-3})-8(\color{red}{-3})-6(\color{red}{-3})[/latex] | |
| [latex]11-20\stackrel{\text{?}}{=}-51+24+18[/latex] | |
| [latex]-9=-9\quad\checkmark[/latex] | |
example
Solve: [latex]-3\left(n - 2\right)-6=21[/latex]
Remember—always simplify each side first.
Answer:
Solution:
| [latex]-3(n-2)-6=21[/latex] |
| Distribute. | [latex]-3n+6-6=21[/latex] |
| Simplify. | [latex]-3n=21[/latex] |
| Divide both sides by -3 to isolate n. | [latex]\Large\frac{-3n}{\color{red}{-3}}\normalsize =\Large\frac{21}{\color{red}{-3}}[/latex][latex]n=-7[/latex]
|
| Check your answer. Let [latex]n=-7[/latex] . | |
| [latex]-3(n-2)-6=21[/latex] | |
| [latex]-3(\color{red}{-7}-2)-6\stackrel{\text{?}}{=}21[/latex] | |
| [latex]-3(-9)-6\stackrel{\text{?}}{=}21[/latex] | |
| [latex]27-6\stackrel{\text{?}}{=}21[/latex] | |
| [latex]21=21\quad\checkmark[/latex] | |
