Multi-Step Equations 2

Question 1 of 3

Solve

\frac{4 - 4 z}{2} = 8

$(4-4z)/2=8$

$z =$ $z=$ (-3)

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Inverse Operations

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

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

Start with removing

\frac{1}{2}

$1/2$ by multiplying both sides of the equation by

2

$2$ .

$\frac{4-4\color{#00880A}{z}}{2}$	$=$ $=$	$8$ $8$

$\frac{4-4\color{#00880A}{z}}{2}\color{#CC0000}{\times2}$	$=$ $=$	$8$ $8$ $\times 2$ $times2$

$4 - 4$ $4-4$ $z$ $z$	$=$ $=$	$16$ $16$	$\frac{1}{2} \times 2$ $1/2 times2$ cancels out

Next, move

4

$4$ to the other side by subtracting

4

$4$ from both sides of the equation.

$4 - 4$ $4-4$ $z$ $z$	$=$ $=$	$16$ $16$

$4 - 4$ $4-4$ $z$ $z$ $- 4$ $-4$	$=$ $=$	$16$ $16$ $- 4$ $-4$

$- 4$ $-4$ $z$ $z$	$=$ $=$	$12$ $12$	$4 - 4$ $4-4$ cancels out

Finally, remove

- 4

$-4$ by dividing both sides of the equation by

- 4

$-4$ .

$- 4$ $-4$ $z$ $z$	$=$ $=$	$12$ $12$
$- 4$ $-4$ $z$ $z$ $\div - 4$ $divide-4$	$=$ $=$	$12$ $12$ $\div - 4$ $divide-4$
$z$ $z$	$=$ $=$	$- 3$ $-3$	$- 4 \div - 4$ $-4divide-4$ cancels out

Check our work

To confirm our answer, substitute

z = - 3

$z=-3$ to the original equation.

$\frac{4 - 4 z}{2}$ $(4-4z)/2$	$=$ $=$	$8$ $8$

$\frac{4 - 4 (- 3)}{2}$ $(4-4(-3))/2$	$=$ $=$	$8$ $8$	Substitute $z = - 3$ $z=-3$

$\frac{4 + 12}{2}$ $(4+12)/2$	$=$ $=$	$8$ $8$

$\frac{16}{2}$ $16/2$	$=$ $=$	$8$ $8$

$8$ $8$	$=$ $=$	$8$ $8$

Since the equation is true, the answer is correct.

z = - 3

$z=-3$

Question 2 of 3

Solve

\frac{3 y + 4}{- 2} = 7

$(3y+4)/(-2)=7$

$y =$ $y=$ (-6)

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Inverse Operations

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

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

Start with removing

\frac{1}{- 2}

$1/(-2)$ by multiplying both sides of the equation by

- 2

$-2$ .

$\frac{3\color{#00880A}{y}+4}{-2}$	$=$ $=$	$7$ $7$

$\frac{3\color{#00880A}{y}+4}{-2}\color{#CC0000}{\times(-2)}$	$=$ $=$	$7$ $7$ $\times (- 2)$ $times(-2)$

$3$ $3$ $y$ $y$ $+ 4$ $+4$	$=$ $=$	$- 14$ $-14$	$\frac{1}{- 2} \times (- 2)$ $1/(-2) times(-2)$ cancels out

Next, move

4

$4$ to the other side by subtracting

4

$4$ from both sides of the equation.

$3$ $3$ $y$ $y$ $+ 4$ $+4$	$=$ $=$	$- 14$ $-14$

$3$ $3$ $y$ $y$ $+ 4$ $+4$ $- 4$ $-4$	$=$ $=$	$- 14$ $-14$ $- 4$ $-4$

$3$ $3$ $y$ $y$	$=$ $=$	$- 18$ $-18$	$4 - 4$ $4-4$ cancels out

Finally, remove

3

$3$ by dividing both sides of the equation by

3

$3$ .

$3$ $3$ $y$ $y$	$=$ $=$	$- 18$ $-18$
$3$ $3$ $y$ $y$ $\div 3$ $divide3$	$=$ $=$	$- 18$ $-18$ $\div 3$ $divide3$
$y$ $y$	$=$ $=$	$- 6$ $-6$	$3 \div 3$ $3divide3$ cancels out

Check our work

To confirm our answer, substitute

y = - 6

$y=-6$ to the original equation.

$\frac{3 y + 4}{- 2}$ $(3y+4)/(-2)$	$=$ $=$	$7$ $7$

$\frac{3 (- 6) + 4}{- 2}$ $(3(-6)+4)/(-2)$	$=$ $=$	$7$ $7$	Substitute $y = - 6$ $y=-6$

$\frac{- 18 + 4}{- 2}$ $(-18+4)/(-2)$	$=$ $=$	$7$ $7$

$\frac{- 14}{- 2}$ $(-14)/(-2)$	$=$ $=$	$7$ $7$

$7$ $7$	$=$ $=$	$7$ $7$

Since the equation is true, the answer is correct.

y = - 6

$y=-6$

Question 3 of 3

Solve

\frac{8 x - 2}{- 5} = - 6

$(8x-2)/(-5)=-6$

$x =$ $x=$ (4)

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Inverse Operations

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

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

Start with removing

\frac{1}{- 5}

$1/(-5)$ by multiplying both sides of the equation by

- 5

$-5$ .

$\frac{8\color{#00880A}{x}-2}{-5}$	$=$ $=$	$- 6$ $-6$

$\frac{8\color{#00880A}{x}-2}{-5}\color{#CC0000}{\times(-5)}$	$=$ $=$	$- 6$ $-6$ $\times (- 5)$ $times(-5)$

$8$ $8$ $x$ $x$ $- 2$ $-2$	$=$ $=$	$30$ $30$	$\frac{1}{- 5} \times (- 5)$ $1/(-5) times(-5)$ cancels out

Next, move

- 2

$-2$ to the other side by adding

2

$2$ to both sides of the equation.

$8$ $8$ $x$ $x$ $- 2$ $-2$	$=$ $=$	$30$ $30$

$8$ $8$ $x$ $x$ $- 2$ $-2$ $+ 2$ $+2$	$=$ $=$	$30$ $30$ $+ 2$ $+2$

$8$ $8$ $x$ $x$	$=$ $=$	$32$ $32$	$- 2 + 2$ $-2+2$ cancels out

Finally, remove

8

$8$ by dividing both sides of the equation by

8

$8$ .

$8$ $8$ $x$ $x$	$=$ $=$	$32$ $32$
$8$ $8$ $x$ $x$ $\div 8$ $divide8$	$=$ $=$	$32$ $32$ $\div 8$ $divide8$
$x$ $x$	$=$ $=$	$4$ $4$	$8 \div 8$ $8divide8$ cancels out

Check our work

To confirm our answer, substitute

x = 4

$x=4$ to the original equation.

$\frac{8 x - 2}{- 5}$ $(8x-2)/(-5)$	$=$ $=$	$- 6$ $-6$

$\frac{8 (4) - 2}{- 5}$ $(8(4)-2)/(-5)$	$=$ $=$	$- 6$ $-6$	Substitute $x = 4$ $x=4$

$\frac{32 - 2}{- 5}$ $(32-2)/(-5)$	$=$ $=$	$- 6$ $-6$

$\frac{30}{- 5}$ $(30)/(-5)$	$=$ $=$	$- 6$ $-6$

$- 6$ $-6$	$=$ $=$	$- 6$ $-6$

Since the equation is true, the answer is correct.

x = 4

$x=4$

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Quiz summary

Information

1. Question

Hint

Fantastic!

Inverse Operations

2. Question

Hint

Well Done!

Inverse Operations

3. Question

Hint

Keep Going!

Inverse Operations

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