Solve Equations using the Distributive Property 3

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Question 1 of 3

1. Question
Solve for $x$

$2(x+1)=8$
- $x=$ (3)
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To solve for $x$ , get $x$ by itself

Divide both sides of the equation by $2$

$2(x+1)$ $divide2$ $=$ $8$ $divide2$

$2$ $(x+1)$ $divide2$ $=$ $8$ $divide2$ $times2divide2$ cancels out

$x+1$ $=$ $4$

Finally, subtract $1$ from both sides of the equation

$x+1$ $-1$ $=$ $4$ $-1$

$x$ $+1$ $-1$ $=$ $4$ $-1$ $1-1$ cancels out

$x$ $=$ $3$

$x=3$
Question 2 of 3

2. Question
Solve for $x$

$2(3-x)=8$
- $x=$ (-1)
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To solve for $x$ , get $x$ by itself

Divide both sides of the equation by $2$

$2(3-x)$ $divide2$ $=$ $8$ $divide2$

$2$ $(3-x)$ $divide2$ $=$ $8$ $divide2$ $times2divide2$ cancels out

$3-x$ $=$ $4$

Next, subtract $3$ from both sides of the equation

$3-x$ $-3$ $=$ $4$ $-3$

$3$ $-x$ $-3$ $=$ $4$ $-3$ $3-3$ cancels out

$-x$ $=$ $1$

Finally, make $x$ positive by dividing both sides by $-1$

$-x$ $divide(-1)$ $=$ $1$ $divide(-1)$

$x$ $=$ $-1$

$x=-1$

Question 3 of 3

Solve

$(-(9n-6))/4=-3$

$n=$ (2)

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Inverse Operations

When moving a term to the other side of an equation, the operation is inversed.

To solve for $n$ , it needs to be alone on one side.

Start with removing

$1/4$ by multiplying both sides of the equation by

$4$ .

$\frac{-(9\color{#00880A}{n}-6)}{4}$	$=$	$-3$

$\frac{-(9\color{#00880A}{n}-6)}{4}\color{#CC0000}{\times4}$	$=$	$-3$ $times4$

$-(9$ $n$ $-6)$	$=$	$-12$	$1/4 times4$ cancels out
$-9$ $n$ $+6$	$=$	$-12$

Next, move

$6$ to the other side by subtracting

$6$ from both sides of the equation.

$-9$ $n$ $+6$	$=$	$-12$
$-9$ $n$ $+6$ $-6$	$=$	$-12$ $-6$
$-9$ $n$	$=$	$-18$	$6-6$ cancels out

Finally, remove

$-9$ by dividing both sides of the equation by

$-9$ .

$-9$ $n$	$=$	$-18$
$-9$ $n$ $divide-9$	$=$	$-18$ $divide-9$
$n$	$=$	$2$	$-9divide-9$ cancels out

Check our work

To confirm our answer, substitute

$n=2$ to the original equation.

$(-(9n-6))/4$	$=$	$-3$

$(-(9(2)-6))/4$	$=$	$-3$	Substitute $n=2$

$(-(18-6))/4$	$=$	$-3$

$(-12)/4$	$=$	$-3$

$-3$	$=$	$-3$

Since the equation is true, the answer is correct.

$n=2$

Solve Equations using the Distributive Property 3

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Quiz summary

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1. Question

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Great Work!

2. Question

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3. Question

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Inverse Operations

Quizzes

$2(x+1)$ $divide2$	$=$	$8$ $divide2$
$2$ $(x+1)$ $divide2$	$=$	$8$ $divide2$	$times2divide2$ cancels out
$x+1$	$=$	$4$

$x+1$ $-1$	$=$	$4$ $-1$
$x$ $+1$ $-1$	$=$	$4$ $-1$	$1-1$ cancels out
$x$	$=$	$3$

$2(3-x)$ $divide2$	$=$	$8$ $divide2$
$2$ $(3-x)$ $divide2$	$=$	$8$ $divide2$	$times2divide2$ cancels out
$3-x$	$=$	$4$

$3-x$ $-3$	$=$	$4$ $-3$
$3$ $-x$ $-3$	$=$	$4$ $-3$	$3-3$ cancels out
$-x$	$=$	$1$