Solve Equations using the Distributive Property 2

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Question 1 of 4

Solve

- 7 (3 - y) = - 28

$-7(3-y)=-28$

$y =$ $y=$ (-1)

Question 2 of 4

2. Question
Solve for $x$ $x$

$5 - (3 - 2 x) = 10$ $5-(3-2x)=10$
- $x =$ $x=$ (4)
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To solve for $x$ $x$ , get $x$ $x$ by itself

Subtract $5$ $5$ from both sides of the equation

$5 - (3 - 2 x)$ $5-(3-2x)$ $- 5$ $-5$ $=$ $=$ $10$ $10$ $- 5$ $-5$

$5$ $5$ $- (3 - 2 x)$ $-(3-2x)$ $- 5$ $-5$ $=$ $=$ $10$ $10$ $- 5$ $-5$ $5 - 5$ $5-5$ cancels out

$- 3 + 2 x$ $-3+2x$ $=$ $=$ $5$ $5$ Distribute negative sign

Next, add $3$ $3$ to both sides of the equation

$- 3 + 2 x$ $-3+2x$ $+ 3$ $+3$ $=$ $=$ $5$ $5$ $+ 3$ $+3$

$- 3$ $-3$ $+ 2 x$ $+2x$ $+ 3$ $+3$ $=$ $=$ $5$ $5$ $+ 3$ $+3$ $- 3 + 3$ $-3+3$ cancels out

$2 x$ $2x$ $=$ $=$ $8$ $8$

Finally, divide both sides of the equation by $2$ $2$

$2 x$ $2x$ $\div 2$ $divide2$ $=$ $=$ $8$ $8$ $\div 2$ $divide2$

$2$ $2$ $x$ $x$ $\div 2$ $divide2$ $=$ $=$ $8$ $8$ $\div 2$ $divide2$ $\times 2 \div 2$ $times2divide2$ cancels out

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

$x = 4$ $x=4$

Question 3 of 4

Solve for

k

$k$

- 9 (- 8 + k) = 252

$-9(-8+k)=252$

$k =$ $k=$ (-20)

Question 4 of 4

Solve for

a

$a$

- 12 (a + 11) = - 108

$-12(a+11)=-108$

$a =$ $a=$ (-2)

$- 7$ $-7$ $(3 -$ $(3-$ $y$ $y$ $)$ $)$	$=$ $=$	$- 28$ $-28$
$- 7$ $-7$ $(3) - ($ $(3)-($ $- 7$ $-7$ $) ($ $)($ $y$ $y$ $)$ $)$	$=$ $=$	$- 28$ $-28$
$- 21 + 7$ $-21+7$ $y$ $y$	$=$ $=$	$- 28$ $-28$

$- 21 + 7$ $-21+7$ $y$ $y$	$=$ $=$	$- 28$ $-28$
$- 21 + 7$ $-21+7$ $y$ $y$ $+ 21$ $+21$	$=$ $=$	$- 28$ $-28$ $+ 21$ $+21$
$7$ $7$ $y$ $y$	$=$ $=$	$- 7$ $-7$	$- 21 + 21$ $-21+21$ cancels out

$7$ $7$ $y$ $y$	$=$ $=$	$- 7$ $-7$
$7$ $7$ $y$ $y$ $\div 7$ $divide7$	$=$ $=$	$- 7$ $-7$ $\div 7$ $divide7$
$y$ $y$	$=$ $=$	$- 1$ $-1$	$7 \div 7$ $7divide7$ cancels out

$- 7 (3 - y)$ $-7(3-y)$	$=$ $=$	$- 28$ $-28$
$- 7 [3 - (- 1)]$ $-7[3-(-1)]$	$=$ $=$	$- 28$ $-28$	Substitute $y = - 1$ $y=-1$
$- 7 (3 + 1)$ $-7(3+1)$	$=$ $=$	$- 28$ $-28$
$- 7 (4)$ $-7(4)$	$=$ $=$	$- 28$ $-28$
$- 28$ $-28$	$=$ $=$	$- 28$ $-28$

$- 9$ $-9$ $(- 8 + k)$ $(-8+k)$	$=$ $=$	$252$ $252$
$((- 8) \times$ $((-8)xx$ $(- 9)$ $(-9)$ $) + (k \times$ $)+(kxx$ $(- 9)$ $(-9)$ $)$ $)$	$=$ $=$	$252$ $252$
$72 - 9 k$ $72-9k$	$=$ $=$	$252$ $252$

Solve Equations using the Distributive Property 2

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Quiz summary

Information

1. Question

Hint

Great Work!

Inverse Operations

Distributive Property

2. Question

Hint

Correct!

3. Question

Fantastic!

4. Question

Exceptional!

Quizzes

$5 - (3 - 2 x)$ $5-(3-2x)$ $- 5$ $-5$	$=$ $=$	$10$ $10$ $- 5$ $-5$
$5$ $5$ $- (3 - 2 x)$ $-(3-2x)$ $- 5$ $-5$	$=$ $=$	$10$ $10$ $- 5$ $-5$	$5 - 5$ $5-5$ cancels out
$- 3 + 2 x$ $-3+2x$	$=$ $=$	$5$ $5$	Distribute negative sign

$- 3 + 2 x$ $-3+2x$ $+ 3$ $+3$	$=$ $=$	$5$ $5$ $+ 3$ $+3$
$- 3$ $-3$ $+ 2 x$ $+2x$ $+ 3$ $+3$	$=$ $=$	$5$ $5$ $+ 3$ $+3$	$- 3 + 3$ $-3+3$ cancels out
$2 x$ $2x$	$=$ $=$	$8$ $8$

$2 x$ $2x$ $\div 2$ $divide2$	$=$ $=$	$8$ $8$ $\div 2$ $divide2$
$2$ $2$ $x$ $x$ $\div 2$ $divide2$	$=$ $=$	$8$ $8$ $\div 2$ $divide2$	$\times 2 \div 2$ $times2divide2$ cancels out
$x$ $x$	$=$ $=$	$4$ $4$

$72 - 9 k$ $72-9k$ $- 72$ $-72$	$=$ $=$	$252$ $252$ $- 72$ $-72$	Subtract $72$ $72$ from both sides
$72$ $72$ $- 9 k$ $-9k$ $- 72$ $-72$	$=$ $=$	$252$ $252$ $- 72$ $-72$	$72 - 72$ $72-72$ cancels out
$- 9 k$ $-9k$	$=$ $=$	$180$ $180$
$- 9 k$ $-9k$ $\div (- 9)$ $-:(-9)$	$=$ $=$	$180$ $180$ $\div (- 9)$ $-:(-9)$	Divide both sides by $- 9$ $-9$
$- 9$ $-9$ $k$ $k$ $\div (- 9)$ $-:(-9)$	$=$ $=$	$180$ $180$ $\div (- 9)$ $-:(-9)$	$\times (- 9) \div (- 9)$ $times(-9)divide(-9)$ cancels out
$k$ $k$	$=$ $=$	$- 20$ $-20$

$- 12$ $-12$ $(a + 11)$ $(a+11)$	$=$ $=$	$- 108$ $-108$
$(a \times$ $(axx$ $(- 12)$ $(-12)$ $) + (11 \times$ $)+(11xx$ $(- 12)$ $(-12)$ $)$ $)$	$=$ $=$	$- 108$ $-108$
$- 12 a - 132$ $-12a-132$	$=$ $=$	$- 108$ $-108$

$- 12 a - 132$ $-12a-132$ $+ 132$ $+132$	$=$ $=$	$- 108$ $-108$ $+ 132$ $+132$	Add $132$ $132$ to both sides
$- 12 a$ $-12a$ $- 132$ $-132$ $+ 132$ $+132$	$=$ $=$	$- 108$ $-108$ $+ 132$ $+132$	$- 132 + 132$ $-132+132$ cancels out
$- 12 a$ $-12a$	$=$ $=$	$24$ $24$
$- 12 a$ $-12a$ $\div (- 12)$ $divide(-12)$	$=$ $=$	$24$ $24$ $\div (- 12)$ $divide(-12)$	Divide both sides by $- 12$ $-12$
$- 12$ $-12$ $a$ $a$ $\div (- 12)$ $divide(-12)$	$=$ $=$	$24$ $24$ $\div (- 12)$ $divide(-12)$	$\times (- 12) \div (- 12)$ $times(-12)divide(-12)$ cancels out
$a$ $a$	$=$ $=$	$- 2$ $-2$