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] | |
Here is a similar problem for you to try.
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] | |
Notice that the variable ended up on the right side of the equal sign when we solved the equation. You may prefer to take one more step to write the solution with the variable on the left side of the equal sign.
Now you can try solving a similar problem.
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] | |
Now you can try a similar problem.