Solve Equations with Variables on Both Sides using the Distributive Property 2

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Question 1 of 5

Solve

7 (m + 2) + 2 (6 - 2 m) = 4 m

$7(m+2)+2(6-2m)=4m$

$m =$ $m=$ (26)

Question 2 of 5

Solve

2 (y + 3) + 5 (y + 2) = 4 (9 - 4 y) - 3 (16 - 3 y)

$2(y+3)+5(y+2)=4(9-4y)-3(16-3y)$

$y =$ $y=$ (-2)

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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

$c$

Get $y$ $y$ alone to the left side and all constants to the right.

Start by expanding both sides of the equation by using the Distributive Property.

$2$ $2$ $($ $($ $y$ $y$ $+ 3) +$ $+3)+$ $5$ $5$ $($ $($ $y$ $y$ $+ 2)$ $+2)$	$=$ $=$	$4$ $4$ $(9 - 4$ $(9-4$ $y$ $y$ $) -$ $)-$ $3$ $3$ $(16 - 3$ $(16-3$ $y$ $y$ $)$ $)$
$2$ $2$ $y$ $y$ $+$ $+$ $2$ $2$ $(3) +$ $(3)+$ $5$ $5$ $y$ $y$ $+$ $+$ $5$ $5$ $(2)$ $(2)$	$=$ $=$	$4$ $4$ $(9) -$ $(9)-$ $4$ $4$ $(4$ $(4$ $y$ $y$ $) -$ $)-$ $3$ $3$ $(16) -$ $(16)-$ $3$ $3$ $(- 3$ $(-3$ $y$ $y$ $)$ $)$
$2$ $2$ $y$ $y$ $+ 6 + 5$ $+6+5$ $y$ $y$ $+ 10$ $+10$	$=$ $=$	$36 - 16$ $36-16$ $y$ $y$ $- 48 + 9$ $-48+9$ $y$ $y$
$7$ $7$ $y$ $y$ $+ 16$ $+16$	$=$ $=$	$- 7$ $-7$ $y$ $y$ $- 12$ $-12$

Next, move

16

$16$ to the other side by subtracting

16

$16$ from both sides of the equation.

$7$ $7$ $y$ $y$ $+ 16$ $+16$	$=$ $=$	$- 7$ $-7$ $y$ $y$ $- 12$ $-12$
$7$ $7$ $y$ $y$ $+ 16$ $+16$ $- 16$ $-16$	$=$ $=$	$- 7$ $-7$ $y$ $y$ $- 12$ $-12$ $- 16$ $-16$
$7$ $7$ $y$ $y$	$=$ $=$	$- 7$ $-7$ $y$ $y$ $- 28$ $-28$	$16 - 16$ $16-16$ cancels out

Then, move

- 7 y

$-7y$ to the other side by adding

7 y

$7y$ to both sides of the equation.

$7$ $7$ $y$ $y$	$=$ $=$	$- 7$ $-7$ $y$ $y$ $- 28$ $-28$
$7$ $7$ $y$ $y$ $+ 7 y$ $+7y$	$=$ $=$	$- 7$ $-7$ $y$ $y$ $- 28$ $-28$ $+ 7 y$ $+7y$
$14$ $14$ $y$ $y$	$=$ $=$	$- 28$ $-28$	$- 7 y + 7 y$ $-7y+7y$ cancels out

Finally, remove

14

$14$ by dividing both sides of the equation by

14

$14$ .

$14$ $14$ $y$ $y$	$=$ $=$	$- 28$ $-28$
$14$ $y$ $-:14$	$=$	$-28$ $-:14$
$y$	$=$	$-2$	$14divide14$ cancels out

Check our work

To confirm our answer, substitute

$y=-2$ to the original equation.

$2(y+3)+5(y+2)$	$=$	$4(9-4y)-3(16-3y)$
$2(-2+3)+5(-2+2)$	$=$	$4(9-4(-2))-3(16-3(-2))$	Substitute $y=-2$
$2(1)+5(0)$	$=$	$4(9+8)-3(16+6)$
$2+0$	$=$	$4(17)-3(22)$
$2$	$=$	$68-66$
$2$	$=$	$2$

Since the equation is true, the answer is correct.

$y=-2$

Question 3 of 5

Solve for

$x$

$6(x+2)-4(x-1)=20$

$x=$ (2)

Question 4 of 5

Solve for

$v$

$-8v+7(v+8)=32-7v$

$v=$ (-4)

Question 5 of 5

Solve for

$k$

$11-5k=4+7(1-5k)$

$k=$ (0)

$7$ $7$ $($ $($ $m$ $m$ $+ 2) +$ $+2)+$ $2$ $2$ $(6 - 2$ $(6-2$ $m$ $m$ $)$ $)$	$=$ $=$	$4$ $4$ $m$ $m$
$7$ $7$ $m$ $m$ $+$ $+$ $7$ $7$ $(2) +$ $(2)+$ $2$ $2$ $(6) +$ $(6)+$ $2$ $2$ $(- 2$ $(-2$ $m$ $m$ $)$ $)$	$=$ $=$	$4$ $4$ $m$ $m$
$7$ $7$ $m$ $m$ $+ 14 + 12 - 4$ $+14+12-4$ $m$ $m$	$=$ $=$	$4$ $4$ $m$ $m$
$3$ $3$ $m$ $m$ $+ 26$ $+26$	$=$ $=$	$4$ $4$ $m$ $m$

$3$ $3$ $m$ $m$ $+ 26$ $+26$	$=$ $=$	$4$ $4$ $m$ $m$
$3$ $3$ $m$ $m$ $+ 26$ $+26$ $- 3 m$ $-3m$	$=$ $=$	$4$ $4$ $m$ $m$ $- 3 m$ $-3m$
$26$ $26$	$=$ $=$	$m$ $m$	$3 m - 3 m$ $3m-3m$ cancels out
$m$ $m$	$=$ $=$	$26$ $26$

$7 (m + 2) + 2 (6 - 2 m)$ $7(m+2)+2(6-2m)$	$=$ $=$	$4 m$ $4m$
$7 (26 + 2) + 2 (6 - 2 (26))$ $7(26+2)+2(6-2(26))$	$=$ $=$	$4 (26)$ $4(26)$	Substitute $m = 26$ $m=26$
$7 (28) + 2 (6 - 52)$ $7(28)+2(6-52)$	$=$ $=$	$104$ $104$
$196 + 2 (- 46)$ $196+2(-46)$	$=$ $=$	$104$ $104$
$196 - 92$ $196-92$	$=$ $=$	$104$ $104$
$104$ $104$	$=$ $=$	$104$ $104$

$6$ $(x+2)$ $-4$ $(x-1)$	$=$	$20$

$6$ $(x+2)$	$=$	$(x xx$ $6$ $)+(2xx$ $6$ $)$
	$=$	$6x+12$

$-4$ $(x-1)$	$=$	$(x xx$ $(-4)$ $)+(-1xx$ $(-4)$ $)$
	$=$	$-4x+4$

$(6x+12)$ $+$ $(-4x+4)$	$=$	$20$
$2x+16$	$=$	$20$

$2x+16$ $-16$	$=$	$20$ $-16$
$2x$ $+16$ $-16$	$=$	$20$ $-16$	$16-16$ cancels out
$2x$	$=$	$4$
$2x$ $divide2$	$=$	$4$ $divide2$	Divide both sides by $2$
$2$ $x$ $divide2$	$=$	$4$ $divide2$	$times2divide2$ cancels out
$x$	$=$	$2$

Solve Equations with Variables on Both Sides using the Distributive Property 2

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Quiz summary

Information

1. Question

Hint

Excellent!

Inverse Operations

Distributive Property

2. Question

Hint

Fantastic!

Inverse Operations

Distributive Property

3. Question

Hint

Correct!

4. Question

5. Question

Well Done!

Quizzes

$-8v$ $+7$ $(v+8)$	$=$	$32-7v$
$-8v+((v xx$ $7$ $)+(8xx$ $7$ $))$	$=$	$32-7v$
$-8v+7v+56$	$=$	$32-7v$
$-v+56$	$=$	$32-7v$

$-v+56$ $+7v$	$=$	$32-7v$ $+7v$	Add $7v$ to both sides
$-v+56$ $+7v$	$=$	$32$ $-7v$ $+7v$	$-7v+7v$ cancels out
$6v+56$	$=$	$32$
$6v+56$ $-56$	$=$	$32$ $-56$	Subtract $56$ from both sides
$6v$ $+56$ $-56$	$=$	$32$ $-56$	$56-56$ cancels out
$6v$	$=$	$-24$
$6v$ $-:6$	$=$	$-24$ $-:6$	Divide both sides by $6$
$6$ $v$ $-:6$	$=$	$-24$ $-:6$	$times6divide6$ cancels out
$v$	$=$	$-4$

$11-5k$	$=$	$4$ $+7$ $(1-5k)$
$11-5k$	$=$	$4+((1 xx$ $7$ $)+(-5k xx$ $7$ $))$
$11-5k$	$=$	$4+7-35k$
$11-5k$	$=$	$11-35k$

$11-5k$ $+5k$	$=$	$11-35k$ $+5k$	Add $5k$ to both sides
$11$ $-5k$ $+5k$	$=$	$11-35k$ $+5k$	$-5k+5k$ cancels out
$11$	$=$	$11-30k$
$11$ $-11$	$=$	$11-30k$ $-11$	Subtract $11$ from both sides
$11$ $-11$	$=$	$11$ $-30k$ $-11$	$11-11$ cancels out on both sides
$0$	$=$	$-30k$
$0$ $-:(-30)$	$=$	$30k$ $-:(-30)$	Divide both sides by $-30$
$0$ $-:(-30)$	$=$	$30$ $k$ $-:(-30)$	$times(-30)divide(-30)$ cancels out
$0$	$=$	$k$
$k$	$=$	$0$