Multi-Step Equations 1

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Year 8

Equations

Multi-Step Equations

Multi-Step Equations 1

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Question 1 of 4

1. Question
Solve

$\frac{4}{5} x - 9 = - 1$ $4/5 x-9=-1$
- $x =$ $x=$ (10)
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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 by moving $- 9$ $-9$ to the other side by adding $9$ $9$ to both sides of the equation.

$\frac{4}{5}$ $4/5$ $x$ $x$ $- 9$ $-9$ $=$ $=$ $- 1$ $-1$

$\frac{4}{5}$ $4/5$ $x$ $x$ $- 9$ $-9$ $+ 9$ $+9$ $=$ $=$ $- 1$ $-1$ $+ 9$ $+9$

$\frac{4}{5}$ $4/5$ $x$ $x$ $=$ $=$ $8$ $8$ $- 9 + 9$ $-9+9$ cancels out

Next, remove $\frac{1}{5}$ $1/5$ by multiplying both sides of the equation by $5$ $5$ .

$\frac{4}{5}$ $4/5$ $x$ $x$ $=$ $=$ $8$ $8$

$\frac{4}{5}$ $4/5$ $x$ $x$ $\times 5$ $times5$ $=$ $=$ $8$ $8$ $\times 5$ $times5$

$4$ $4$ $x$ $x$ $=$ $=$ $40$ $40$ $\frac{1}{5} \times 5$ $1/5 times5$ cancels out

Finally, remove $4$ $4$ by dividing both sides of the equation by $4$ $4$ .

$4$ $4$ $x$ $x$ $=$ $=$ $40$ $40$

$4$ $4$ $x$ $x$ $\div 4$ $divide4$ $=$ $=$ $40$ $40$ $\div 4$ $divide4$

$x$ $x$ $=$ $=$ $10$ $10$ $4 \div 4$ $4divide4$ cancels out

Check our work

To confirm our answer, substitute $x = 10$ $x=10$ to the original equation.

$\frac{4}{5} x - 9$ $4/5 x-9$ $=$ $=$ $- 1$ $-1$

$\frac{4}{5} (10) - 9$ $4/5 (10)-9$ $=$ $=$ $- 1$ $-1$ Substitute $x = 10$ $x=10$

$\frac{40}{5} - 9$ $40/5-9$ $=$ $=$ $- 1$ $-1$

$8 - 9$ $8-9$ $=$ $=$ $- 1$ $-1$

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

Since the equation is true, the answer is correct.

$x = 10$ $x=10$

Question 2 of 4

Solve

\frac{2 m}{3} + 8 = 10

$(2m)/3+8=10$

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

Start by moving

8

$8$ to the other side by subtracting

8

$8$ from both sides of the equation.

$\frac{2\color{#00880A}{m}}{3}+8$	$=$ $=$	$10$ $10$

$\frac{2\color{#00880A}{m}}{3}+8 \color{#CC0000}{-8}$	$=$ $=$	$10$ $10$ $- 8$ $-8$

$\frac{2\color{#00880A}{m}}{3}$	$=$ $=$	$2$ $2$	$8 - 8$ $8-8$ cancels out

Next, remove

\frac{1}{3}

$1/3$ by multiplying both sides of the equation by

3

$3$ .

$\frac{2\color{#00880A}{m}}{3}$	$=$ $=$	$2$ $2$

$\frac{2\color{#00880A}{m}}{3} \color{#CC0000}{\times3}$	$=$ $=$	$2$ $2$ $\times 3$ $times3$

$2$ $2$ $m$ $m$	$=$ $=$	$6$ $6$	$\frac{1}{3} \times 3$ $1/3 times3$ cancels out

Finally, remove

2

$2$ by dividing both sides of the equation by

2

$2$ .

$2$ $2$ $m$ $m$	$=$ $=$	$6$ $6$
$2$ $2$ $m$ $m$ $\div 2$ $divide2$	$=$ $=$	$6$ $6$ $\div 2$ $divide2$
$m$ $m$	$=$ $=$	$3$ $3$	$2 \div 2$ $2divide2$ cancels out

Check our work

To confirm our answer, substitute

m = 3

$m=3$ to the original equation.

$\frac{2 m}{3} + 8$ $(2m)/3+8$	$=$ $=$	$10$ $10$

$\frac{2 (3)}{3} + 8$ $(2(3))/3+8$	$=$ $=$	$10$ $10$	Substitute $m = 3$ $m=3$

$\frac{6}{3} + 8$ $6/3+8$	$=$ $=$	$10$ $10$

$2 + 8$ $2+8$	$=$ $=$	$10$ $10$
$10$ $10$	$=$ $=$	$10$ $10$

Since the equation is true, the answer is correct.

m = 3

$m=3$

Question 3 of 4

3. Question
Solve for $x$ $x$

$\frac{x - 4}{2} = 3$ $(x-4)/2=3$
- $x =$ $x=$ (10)
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To solve for $x$ $x$ , get $x$ $x$ by itself

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

$\frac{x - 4}{2}$ $frac{x-4}{2}$ $\times 2$ $times2$ $=$ $=$ $3$ $3$ $\times 2$ $times2$

$\frac{2 (x - 4)}{2}$ $frac{2(x-4)}{2}$ $=$ $=$ $3$ $3$ $\times 2$ $times2$

$x - 4$ $x-4$ $=$ $=$ $6$ $6$ The coefficient $\frac{2}{2}$ $2/2$ cancels out

Finally, add $4$ $4$ to both sides of the equation

$x - 4$ $x-4$ $+ 4$ $+4$ $=$ $=$ $6$ $6$ $+ 4$ $+4$

$x$ $x$ $- 4$ $-4$ $+ 4$ $+4$ $=$ $=$ $6$ $6$ $+ 4$ $+4$ $- 4 + 4$ $-4+4$ cancels out

$x$ $x$ $=$ $=$ $10$ $10$

$x = 10$ $x=10$
Question 4 of 4

4. Question
Solve for $x$ $x$

$\frac{9 + x}{3} = 5$ $(9+x)/3=5$
- $x =$ $x=$ (6)
Correct

Exceptional!

Incorrect

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

Multiply both sides of the equation by $3$ $3$

$\frac{9 + x}{3}$ $(9+x)/3$ $\times 3$ $xx 3$ $=$ $=$ $5$ $5$ $\times 3$ $xx 3$

$\frac{3 (9 + x)}{3}$ $(3(9+x))/3$ $=$ $=$ $5$ $5$ $\times 3$ $xx 3$

$9 + x$ $9+x$ $=$ $=$ $15$ $15$ The coefficient $\frac{3}{3}$ $3/3$ cancels out

Finally, subtract $9$ $9$ from both sides of the equation

$9 + x$ $9+x$ $- 9$ $-9$ $=$ $=$ $15$ $15$ $- 9$ $-9$

$9$ $9$ $+ x$ $+x$ $- 9$ $-9$ $=$ $=$ $15$ $15$ $- 9$ $-9$ $9 - 9$ $9-9$ cancels out

$x$ $x$ $=$ $=$ $6$ $6$

$x = 6$ $x=6$

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Quiz summary

Information

1. Question

Hint

Nice Job!

Inverse Operations

2. Question

Hint

Excellent!

Inverse Operations

3. Question

Hint

Great Work!

4. Question

Exceptional!

Quizzes

$\frac{4}{5}$ $4/5$ $x$ $x$ $- 9$ $-9$	$=$ $=$	$- 1$ $-1$

$\frac{4}{5}$ $4/5$ $x$ $x$ $- 9$ $-9$ $+ 9$ $+9$	$=$ $=$	$- 1$ $-1$ $+ 9$ $+9$

$\frac{4}{5}$ $4/5$ $x$ $x$	$=$ $=$	$8$ $8$	$- 9 + 9$ $-9+9$ cancels out

$4$ $4$ $x$ $x$	$=$ $=$	$40$ $40$
$4$ $4$ $x$ $x$ $\div 4$ $divide4$	$=$ $=$	$40$ $40$ $\div 4$ $divide4$
$x$ $x$	$=$ $=$	$10$ $10$	$4 \div 4$ $4divide4$ cancels out

$\frac{4}{5} x - 9$ $4/5 x-9$	$=$ $=$	$- 1$ $-1$

$\frac{4}{5} (10) - 9$ $4/5 (10)-9$	$=$ $=$	$- 1$ $-1$	Substitute $x = 10$ $x=10$

$\frac{40}{5} - 9$ $40/5-9$	$=$ $=$	$- 1$ $-1$

$8 - 9$ $8-9$	$=$ $=$	$- 1$ $-1$
$- 1$ $-1$	$=$ $=$	$- 1$ $-1$

$\frac{x - 4}{2}$ $frac{x-4}{2}$ $\times 2$ $times2$	$=$ $=$	$3$ $3$ $\times 2$ $times2$

$\frac{2 (x - 4)}{2}$ $frac{2(x-4)}{2}$	$=$ $=$	$3$ $3$ $\times 2$ $times2$

$x - 4$ $x-4$	$=$ $=$	$6$ $6$	The coefficient $\frac{2}{2}$ $2/2$ cancels out

$x - 4$ $x-4$ $+ 4$ $+4$	$=$ $=$	$6$ $6$ $+ 4$ $+4$
$x$ $x$ $- 4$ $-4$ $+ 4$ $+4$	$=$ $=$	$6$ $6$ $+ 4$ $+4$	$- 4 + 4$ $-4+4$ cancels out
$x$ $x$	$=$ $=$	$10$ $10$

$\frac{9 + x}{3}$ $(9+x)/3$ $\times 3$ $xx 3$	$=$ $=$	$5$ $5$ $\times 3$ $xx 3$

$\frac{3 (9 + x)}{3}$ $(3(9+x))/3$	$=$ $=$	$5$ $5$ $\times 3$ $xx 3$

$9 + x$ $9+x$	$=$ $=$	$15$ $15$	The coefficient $\frac{3}{3}$ $3/3$ cancels out

$9 + x$ $9+x$ $- 9$ $-9$	$=$ $=$	$15$ $15$ $- 9$ $-9$
$9$ $9$ $+ x$ $+x$ $- 9$ $-9$	$=$ $=$	$15$ $15$ $- 9$ $-9$	$9 - 9$ $9-9$ cancels out
$x$ $x$	$=$ $=$	$6$ $6$