Solve Equations using the Distributive Property 3

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Question 1 of 3

1. Question
Solve for $x$ $x$

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

Divide both sides of the equation by $2$ $2$

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

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

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

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

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

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

$x$ $x$ $=$ $=$ $3$ $3$

$x = 3$ $x=3$
Question 2 of 3

2. Question
Solve for $x$ $x$

$2 (3 - x) = 8$ $2(3-x)=8$
- $x =$ $x=$ (-1)
Hint

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Correct

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Incorrect

To solve for $x$ $x$ , get $x$ $x$ by itself

Divide both sides of the equation by $2$ $2$

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

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

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

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

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

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

$- x$ $-x$ $=$ $=$ $1$ $1$

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

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

$x$ $x$ $=$ $=$ $- 1$ $-1$

$x = - 1$ $x=-1$

Question 3 of 3

Solve

\frac{- (9 n - 6)}{4} = - 3

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

$n =$ $n=$ (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 $n$ $n$ , it needs to be alone on one side.

Start with removing

\frac{1}{4}

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

4

$4$ .

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

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

$- (9$ $-(9$ $n$ $n$ $- 6)$ $-6)$	$=$ $=$	$- 12$ $-12$	$\frac{1}{4} \times 4$ $1/4 times4$ cancels out
$- 9$ $-9$ $n$ $n$ $+ 6$ $+6$	$=$ $=$	$- 12$ $-12$

Next, move

6

$6$ to the other side by subtracting

6

$6$ from both sides of the equation.

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

Finally, remove

- 9

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

- 9

$-9$ .

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

Check our work

To confirm our answer, substitute

n = 2

$n=2$ to the original equation.

$\frac{- (9 n - 6)}{4}$ $(-(9n-6))/4$	$=$ $=$	$- 3$ $-3$

$\frac{- (9 (2) - 6)}{4}$ $(-(9(2)-6))/4$	$=$ $=$	$- 3$ $-3$	Substitute $n = 2$ $n=2$

$\frac{- (18 - 6)}{4}$ $(-(18-6))/4$	$=$ $=$	$- 3$ $-3$

$\frac{- 12}{4}$ $(-12)/4$	$=$ $=$	$- 3$ $-3$

$- 3$ $-3$	$=$ $=$	$- 3$ $-3$

Since the equation is true, the answer is correct.

n = 2

$n=2$

Solve Equations using the Distributive Property 3

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Quiz summary

Information

1. Question

Hint

Great Work!

2. Question

Hint

Keep Going!

3. Question

Hint

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Inverse Operations

Quizzes

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

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

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

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

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