Solve Equations – Variables on Both Sides (Distributive Property) 1

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Question 1 of 4

Solve

6 (2 m + 5) - 5 (3 m + 2) = 26

$6(2m+5)-5(3m+2)=26$

$m =$ $m=$ (-2)

Question 2 of 4

Solve

8 (2 y + 3) - 4 (3 y + 2) = 32

$8(2y+3)-4(3y+2)=32$

$y =$ $y=$ (4)

Question 3 of 4

Solve

9 (m + 1) = 3 (m - 3)

$9(m+1)=3(m-3)$

$m =$ $m=$ (-3)

Question 4 of 4

4. Question
Solve

$2 a + 5 = 6 (a - 4) - 3 a$ $2a+5=6(a-4)-3a$
- $a =$ $a=$ (29)
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Inverse Operations

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

Distributive Property

$a$ $a$ $(b + c) =$ $(b+c)=$ $a$ $a$ $b +$ $b+$ $a$ $a$ $c$ $c$

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

Start by expanding the right side of the equation by using the Distributive Property.

$2$ $2$ $a$ $a$ $+ 5$ $+5$ $=$ $=$ $6$ $($ $a$ $-4)-3$ $a$

$2$ $a$ $+5$ $=$ $6$ $a$ $-$ $6$ $(4)-3$ $a$

$2$ $a$ $+5$ $=$ $3$ $a$ $-24$

Next, move $2a$ to the other side by subtracting $2a$ from both sides of the equation.

$2$ $a$ $+5$ $=$ $3$ $a$ $-24$

$2$ $a$ $+5$ $-2a$ $=$ $3$ $a$ $-24$ $-2a$

$5$ $=$ $a$ $-24$ $2a-2a$ cancels out

Now, move $-24$ to the other side by adding $24$ to both sides of the equation.

$5$ $=$ $a$ $-24$

$5$ $+24$ $=$ $a$ $-24$ $+24$

$29$ $=$ $a$ $-24+24$ cancels out

$a$ $=$ $29$

Check our work

To confirm our answer, substitute $a=29$ to the original equation.

$2a+5$ $=$ $6(a-4)-3a$

$2(29)+5$ $=$ $6(29-4)-3(29)$ Substitute $a=29$

$58+5$ $=$ $6(25)-87$

$63$ $=$ $150-87$

$63$ $=$ $63$

Since the equation is true, the answer is correct.

$a=29$

$6$ $6$ $(2$ $(2$ $m$ $m$ $+ 5)$ $+5)$ $- 5$ $-5$ $(3$ $(3$ $m$ $m$ $+ 2)$ $+2)$	$=$ $=$	$26$ $26$
$6$ $6$ $(2$ $(2$ $m$ $m$ $) +$ $)+$ $6$ $6$ $(5)$ $(5)$ $- 5$ $-5$ $(3$ $(3$ $m$ $m$ $)$ $)$ $- 5$ $-5$ $(2)$ $(2)$	$=$ $=$	$26$ $26$
$12$ $12$ $m$ $m$ $+ 30 - 15$ $+30-15$ $m$ $m$ $- 10$ $-10$	$=$ $=$	$26$ $26$
$- 3$ $-3$ $m$ $m$ $+ 20$ $+20$	$=$ $=$	$26$ $26$

$- 3$ $-3$ $m$ $m$ $+ 20$ $+20$	$=$ $=$	$26$ $26$
$- 3$ $-3$ $m$ $m$ $+ 20$ $+20$ $- 20$ $-20$	$=$ $=$	$26$ $26$ $- 20$ $-20$
$- 3$ $-3$ $m$ $m$	$=$ $=$	$6$ $6$	$20 - 20$ $20-20$ cancels out

$- 3$ $-3$ $m$ $m$	$=$ $=$	$6$ $6$
$- 3$ $-3$ $m$ $m$ $\div - 3$ $divide-3$	$=$ $=$	$6$ $6$ $\div - 3$ $divide-3$
$m$ $m$	$=$ $=$	$- 2$ $-2$	$- 3 \div - 3$ $-3divide-3$ cancels out

$6 (2 m + 5) - 5 (3 m + 2)$ $6(2m+5)-5(3m+2)$	$=$ $=$	$26$ $26$
$6 (2 (- 2) + 5) - 5 (3 (- 2) + 2)$ $6(2(-2)+5)-5(3(-2)+2)$	$=$ $=$	$26$ $26$	Substitute $m = - 2$ $m=-2$
$6 (- 4 + 5) - 5 (- 6 + 2)$ $6(-4+5)-5(-6+2)$	$=$ $=$	$26$ $26$
$6 (1) - 5 (- 4)$ $6(1)-5(-4)$	$=$ $=$	$26$ $26$
$6 + 20$ $6+20$	$=$ $=$	$26$ $26$
$26$ $26$	$=$ $=$	$26$ $26$

$8$ $8$ $(2$ $(2$ $y$ $y$ $+ 3) -$ $+3)-$ $4$ $4$ $(3$ $(3$ $y$ $y$ $+ 2)$ $+2)$	$=$ $=$	$32$ $32$
$8$ $8$ $(2$ $(2$ $y$ $y$ $) +$ $)+$ $8$ $8$ $(3)$ $(3)$ $- 4$ $-4$ $(3$ $(3$ $y$ $y$ $)$ $)$ $- 4$ $-4$ $(2)$ $(2)$	$=$ $=$	$32$ $32$
$16$ $16$ $y$ $y$ $+ 24 - 12$ $+24-12$ $y$ $y$ $- 8$ $-8$	$=$ $=$	$32$ $32$
$4$ $4$ $y$ $y$ $+ 16$ $+16$	$=$ $=$	$32$ $32$

Solve Equations – Variables on Both Sides (Distributive Property) 1

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Quiz summary

Information

1. Question

Hint

Great Work!

Inverse Operations

Distributive Property

2. Question

Hint

Well Done!

Inverse Operations

Distributive Property

3. Question

Hint

Good Job!

Inverse Operations

Distributive Property

4. Question

Hint

Good Job!

Inverse Operations

Distributive Property

Quizzes

$4$ $4$ $y$ $y$	$=$ $=$	$16$ $16$
$4$ $4$ $y$ $y$ $\div 4$ $divide4$	$=$ $=$	$16$ $16$ $\div 4$ $divide4$
$y$ $y$	$=$ $=$	$4$ $4$	$4 \div 4$ $4divide4$ cancels out

$8 (2 y + 3) - 4 (3 y + 2)$ $8(2y+3)-4(3y+2)$	$=$ $=$	$32$ $32$
$8 [2 (4) + 3] - 4 [3 (4) + 2]$ $8[2(4)+3]-4[3(4)+2]$	$=$ $=$	$32$ $32$	Substitute $y = 4$ $y=4$
$8 (8 + 3) - 4 (12 + 2)$ $8(8+3)-4(12+2)$	$=$ $=$	$32$ $32$
$8 (11) - 4 (14)$ $8(11)-4(14)$	$=$ $=$	$32$ $32$
$88 - 56$ $88-56$	$=$ $=$	$32$ $32$
$32$ $32$	$=$ $=$	$32$ $32$

$9$ $9$ $($ $($ $m$ $m$ $+ 1)$ $+1)$	$=$ $=$	$3$ $3$ $($ $($ $m$ $m$ $- 3)$ $-3)$
$9$ $9$ $($ $($ $m$ $m$ $) +$ $)+$ $9$ $9$ $(1)$ $(1)$	$=$ $=$	$3$ $3$ $($ $($ $m$ $m$ $) +$ $)+$ $3$ $3$ $(- 3)$ $(-3)$
$9$ $9$ $m$ $m$ $+ 9$ $+9$	$=$ $=$	$3$ $3$ $m$ $m$ $- 9$ $-9$

$9$ $9$ $m$ $m$	$=$ $=$	$3$ $3$ $m$ $m$ $- 18$ $-18$
$9$ $9$ $m$ $m$ $- 3 m$ $-3m$	$=$ $=$	$3$ $3$ $m$ $m$ $- 18$ $-18$ $- 3 m$ $-3m$
$6$ $6$ $m$ $m$	$=$ $=$	$- 18$ $-18$	$3 m - 3 m$ $3m-3m$ cancels out

$9 (m + 1)$ $9(m+1)$	$=$ $=$	$3 (m - 3)$ $3(m-3)$
$9 (- 3 + 1)$ $9(-3+1)$	$=$ $=$	$3 (- 3 - 3)$ $3(-3-3)$	Substitute $m = - 3$ $m=-3$
$9 (- 2)$ $9(-2)$	$=$ $=$	$3 (- 6)$ $3(-6)$
$- 18$ $-18$	$=$ $=$	$- 18$ $-18$

$2$ $2$ $a$ $a$ $+ 5$ $+5$	$=$ $=$	$6$ $($ $a$ $-4)-3$ $a$
$2$ $a$ $+5$	$=$	$6$ $a$ $-$ $6$ $(4)-3$ $a$
$2$ $a$ $+5$	$=$	$3$ $a$ $-24$

$2$ $a$ $+5$	$=$	$3$ $a$ $-24$
$2$ $a$ $+5$ $-2a$	$=$	$3$ $a$ $-24$ $-2a$
$5$	$=$	$a$ $-24$	$2a-2a$ cancels out

$5$	$=$	$a$ $-24$
$5$ $+24$	$=$	$a$ $-24$ $+24$
$29$	$=$	$a$	$-24+24$ cancels out
$a$	$=$	$29$

$2a+5$	$=$	$6(a-4)-3a$
$2(29)+5$	$=$	$6(29-4)-3(29)$	Substitute $a=29$
$58+5$	$=$	$6(25)-87$
$63$	$=$	$150-87$
$63$	$=$	$63$