example
Simplify: [latex]8 - 2\left(x+3\right)[/latex]
Answer:
Solution:
|
[latex]8--2(x+3)[/latex] |
Distribute. |
[latex]8--2\cdot x--2\cdot 3[/latex] |
Multiply. |
[latex]8--2x--6[/latex] |
Combine like terms. |
[latex]--2x+2[/latex] |
example
Simplify: [latex]4\left(x - 8\right)-\left(x+3\right)[/latex]
Answer:
Solution:
|
[latex]4(x--8)--(x+3)[/latex] |
Distribute. |
[latex]4x--32--x--3[/latex] |
Combine like terms. |
[latex]3x--35[/latex] |
example
When [latex]y=10[/latex] evaluate:
1. [latex]6\left(5y+1\right)[/latex]
2. [latex]6\cdot 5y+6\cdot 1[/latex]
Solution:
1. |
|
|
[latex]6\left(5y+1\right)[/latex] |
Substitue [latex]\color{red}{10}[/latex] for y. |
[latex]6(5\cdot\color{red}{10}+1)[/latex] |
Simplify in the parentheses. |
[latex]6\left(51\right)[/latex] |
Multiply. |
[latex]306[/latex] |
2. |
|
|
[latex]6\cdot 5y+6\cdot 1[/latex] |
Substitute [latex]\color {red}{10}[/latex] for y. |
[latex]6\cdot 5\cdot\color {red}{10}+6\cdot 1[/latex] |
Simplify. |
[latex]300+6[/latex] |
Add. |
[latex]306[/latex] |
Notice, the answers are the same. When [latex]y=10[/latex],
[latex]6\left(5y+1\right)=6\cdot 5y+6\cdot 1[/latex].
Try it yourself for a different value of [latex]y[/latex].
example
When [latex]y=3[/latex], evaluate
1. [latex]-2\left(4y+1\right)[/latex]
2. [latex]-2\cdot 4y+\left(-2\right)\cdot 1[/latex]
Answer:
Solution:
1. |
|
|
[latex]-2\left(4y+1\right)[/latex] |
Substitute [latex]\color{red}{3}[/latex] for y. |
[latex]--2(4\cdot\color{red}{3}+1)[/latex] |
Simplify in the parentheses. |
[latex]-2\left(13\right)[/latex] |
Multiply. |
[latex]-26[/latex] |
2. |
|
|
[latex]-2\cdot 4y+\left(-2\right)\cdot 1[/latex] |
Substitute [latex]\color{red}{3}[/latex] for y. |
[latex]--2\cdot 4\cdot\color{red}{3}+(--2)\cdot 1[/latex] |
Multiply. |
[latex]-24 - 2[/latex] |
Subtract. |
[latex]-26[/latex] |
The answers are the same. When [latex]y=3[/latex], |
[latex]-2\left(4y+1\right)=-8y - 2[/latex] |
example
When [latex]y=35[/latex] evaluate
1. [latex]\text{-}\left(y+5\right)[/latex] and 2. [latex]\text{-}\mathit{\text{y}}-5[/latex] to show that [latex]-\left(y+5\right)=\text{-}\mathit{\text{y}}-5[/latex]
Answer:
Solution:
1. |
|
|
[latex]\text{-}\left(y+5\right)[/latex] |
Substitute [latex]\color{red}{35}[/latex] for y. |
[latex]--(\color{red}{35}+5)[/latex] |
Add in the parentheses. |
[latex]-\left(40\right)[/latex] |
Simplify. |
[latex]-40[/latex] |
2. |
|
|
[latex]-y - 5[/latex] |
Substitute [latex]\color{red}{35}[/latex] for y. |
[latex]--\color{red}{35}--5[/latex] |
Simplify. |
[latex]-40[/latex] |
The answers are the same when [latex]y=35[/latex], demonstrating that |
[latex]-\left(y+5\right)=\text{-}y - 5[/latex] |