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Solve Equations with Variables on Both Sides using the Distributive Property

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Solve Equations – Variables on Both Sides (Distributive Property) 4

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Question 1 of 5

Solve for

a

$a$

3 (2 a - 4) = 4 a - 6

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

$a =$ $a=$ (3)

Question 2 of 5

Solve for

x

$x$

5 (2 x + 7) - 6 x = 8 + x

$5(2x+7)-6x=8+x$

$x =$ $x=$ (-9)

Question 3 of 5

Solve for

n

$n$

3 (n + 8) = 3 (2 n - 2)

$3(n+8)=3(2n-2)$

$n =$ $n=$ (10)

Question 4 of 5

Solve for

x

$x$

\frac{3 x + 1}{5} = \frac{2 x - 1}{2}

$(3x+1)/5 = (2x-1)/2$

$x =$ $x=$ (7/4)

Question 5 of 5

Solve for

$x$

$(x+3)/6-(x-1)/5=1/3$

$x=$ (11)

$3$ $3$ $(2 a - 4)$ $(2a-4)$	$=$ $=$	$4 a - 6$ $4a-6$
$(2 a \times$ $(2axx$ $3$ $3$ $) - (4 \times$ $)-(4xx$ $3$ $3$ $)$ $)$	$=$ $=$	$4 a - 6$ $4a-6$
$6 a - 12$ $6a-12$	$=$ $=$	$4 a - 6$ $4a-6$

$6 a - 12$ $6a-12$ $- 4 a$ $-4a$	$=$ $=$	$4 a - 6$ $4a-6$ $- 4 a$ $-4a$	Subtract $4 a$ $4a$ from both sides
$6 a - 12$ $6a-12$ $- 4 a$ $-4a$	$=$ $=$	$4 a$ $4a$ $- 6$ $-6$ $- 4 a$ $-4a$	$4 a - 4 a$ $4a-4a$ cancels out
$2 a - 12$ $2a-12$	$=$ $=$	$- 6$ $-6$
$2 a - 12$ $2a-12$ $+ 12$ $+12$	$=$ $=$	$- 6$ $-6$ $+ 12$ $+12$	Add $12$ $12$ to both sides
$2 a$ $2a$ $- 12$ $-12$ $+ 12$ $+12$	$=$ $=$	$- 6$ $-6$ $+ 12$ $+12$	$- 12 + 12$ $-12+12$ cancels out
$2 a$ $2a$	$=$ $=$	$6$ $6$
$2 a$ $2a$ $\div 2$ $divide2$	$=$ $=$	$6$ $6$ $\div 2$ $divide2$	Divide both sides by $2$ $2$
$2$ $2$ $a$ $a$ $\div 2$ $divide2$	$=$ $=$	$6$ $6$ $\div 2$ $divide2$	$\times 2 \div 2$ $times2divide2$ cancels out
$a$ $a$	$=$ $=$	$3$ $3$

$5$ $5$ $(2 x + 7) - 6 x$ $(2x+7)-6x$	$=$ $=$	$8 + x$ $8+x$
$(2 x \times$ $(2x xx$ $5$ $5$ $) + (7 \times$ $)+(7xx$ $5$ $5$ $) - 6 x$ $)-6x$	$=$ $=$	$8 + x$ $8+x$
$10 x + 35 - 6 x$ $10x+35-6x$	$=$ $=$	$8 + x$ $8+x$
$4 x + 35$ $4x+35$	$=$ $=$	$8 + x$ $8+x$

$4 x + 35$ $4x+35$ $- x$ $-x$	$=$ $=$	$8 + x$ $8+x$ $- x$ $-x$	Subtract $x$ $x$ from both sides
$4 x + 35$ $4x+35$ $- x$ $-x$	$=$ $=$	$8$ $8$ $+ x$ $+x$ $- x$ $-x$	$x - x$ $x-x$ cancels out
$3 x + 35$ $3x+35$	$=$ $=$	$8$ $8$
$3 x + 35$ $3x+35$ $- 35$ $-35$	$=$ $=$	$8$ $8$ $- 35$ $-35$	Subtract $35$ $35$ from both sides
$3 x$ $3x$ $+ 35$ $+35$ $- 35$ $-35$	$=$ $=$	$8$ $8$ $- 35$ $-35$	$35 - 35$ $35-35$ cancels out
$3 x$ $3x$	$=$ $=$	$- 27$ $-27$
$3 x$ $3x$ $\div 3$ $divide3$	$=$ $=$	$- 27$ $-27$ $\div 3$ $divide3$	Divide both sides by $3$ $3$
$3$ $3$ $x$ $x$ $\div 3$ $divide3$	$=$ $=$	$- 27$ $-27$ $\div 3$ $divide3$	$\times 3 \div 3$ $times3divide3$ cancels out
$x$ $x$	$=$ $=$	$- 9$ $-9$

$3$ $3$ $(n + 8)$ $(n+8)$	$=$ $=$	$3$ $3$ $(2 n - 2)$ $(2n-2)$
$(n \times$ $(n xx$ $3$ $3$ $) + (8 \times$ $)+(8xx$ $3$ $3$ $)$ $)$	$=$ $=$	$(2 n \times$ $(2n xx$ $3$ $3$ $) + (- 2 \times$ $)+(-2xx$ $3$ $3$ $)$ $)$
$3 n + 24$ $3n+24$	$=$ $=$	$6 n - 6$ $6n-6$

Solve Equations – Variables on Both Sides (Distributive Property) 4

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Quiz summary

Information

1. Question

Hint

Nice Job!

2. Question

Hint

Fantastic!

3. Question

Excellent!

4. Question

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Great Work!

5. Question

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Exceptional!

Quizzes

$3 n + 24$ $3n+24$ $- 24$ $-24$	$=$ $=$	$6 n - 6$ $6n-6$ $- 24$ $-24$	Subtract $24$ $24$ from both sides
$3 n$ $3n$ $+ 24$ $+24$ $- 24$ $-24$	$=$ $=$	$6 n - 6$ $6n-6$ $- 24$ $-24$	$24 - 24$ $24-24$ cancels out
$3 n$ $3n$	$=$ $=$	$6 n - 30$ $6n-30$
$3 n$ $3n$ $- 6 n$ $-6n$	$=$ $=$	$6 n - 30$ $6n-30$ $- 6 n$ $-6n$	Subtract $6 n$ $6n$ from both sides
$3 n$ $3n$ $- 6 n$ $-6n$	$=$ $=$	$6 n$ $6n$ $- 30$ $-30$ $- 6 n$ $-6n$	$6 n - 6 n$ $6n-6n$ cancels out
$- 3 n$ $-3n$	$=$ $=$	$- 30$ $-30$
$- 3 n$ $-3n$ $\div (- 3)$ $divide(-3)$	$=$ $=$	$- 30$ $-30$ $\div (- 3)$ $divide(-3)$	Divide both sides by $- 3$ $-3$
$- 3$ $-3$ $n$ $n$ $\div (- 3)$ $divide(-3)$	$=$ $=$	$- 30$ $-30$ $\div (- 3)$ $divide(-3)$	$\times (- 3) \div (- 3)$ $times(-3)divide(-3)$ cancels out
$n$ $n$	$=$ $=$	$10$ $10$

$\frac{3 x + 1}{5}$ $frac{3x+1}{5}$ $\times 5$ $times5$	$=$ $=$	$\frac{2 x - 1}{2}$ $frac{2x-1}{2}$ $\times 5$ $times5$

$\frac{5 (3 x + 1)}{5}$ $frac{5(3x+1)}{5}$	$=$ $=$	$\frac{2 x - 1}{2}$ $frac{2x-1}{2}$ $\times 5$ $times5$

$3 x + 1$ $3x+1$	$=$ $=$	$\frac{5 (2 x - 1)}{2}$ $frac{5(2x-1)}{2}$	The coefficient $\frac{5}{5}$ $frac{5}{5}$ cancels out

$3 x + 1$ $3x+1$	$=$ $=$	$\frac{(2 x \times 5) - (1 \times 5)}{3}$ $frac{(2x xx 5)-(1xx5)}{3}$	Distribute the value inside the parenthesis

$3 x + 1$ $3x+1$	$=$ $=$	$\frac{2 x - 5}{3}$ $frac{2x-5}{3}$

$(3 x + 1)$ $(3x+1)$ $\times 2$ $times2$	$=$ $=$	$\frac{10 x - 5}{2}$ $frac{10x-5}{2}$ $\times 2$ $times2$

$(3 x + 1)$ $(3x+1)$ $\times 2$ $times2$	$=$ $=$	$\frac{2 (10 x - 5)}{2}$ $frac{2(10x-5)}{2}$

$2 (3 x + 1)$ $2(3x+1)$	$=$ $=$	$10 x - 5$ $10x-5$	The coefficient $\frac{2}{2}$ $frac{2}{2}$ cancels out

$(3 x \times 2) + (1 \times 2)$ $(3x xx 2)+(1xx2)$	$=$ $=$	$10 x - 5$ $10x-5$	Distribute the value inside the parenthesis
$6 x + 2$ $6x+2$	$=$ $=$	$10 x - 5$ $10x-5$

$6 x + 2$ $6x+2$ $- 10 x$ $-10x$	$=$ $=$	$10 x - 5$ $10x-5$ $- 10 x$ $-10x$
$6 x + 2$ $6x+2$ $- 10 x$ $-10x$	$=$ $=$	$10 x$ $10x$ $- 5$ $-5$ $- 10 x$ $-10x$	$10 x - 10 x$ $10x-10x$ cancels out
$- 4 x + 2$ $-4x+2$	$=$ $=$	$- 5$ $-5$

$- 4 x + 2$ $-4x+2$ $- 2$ $-2$	$=$ $=$	$- 5$ $-5$ $- 2$ $-2$
$- 4 x$ $-4x$ $+ 2$ $+2$ $- 2$ $-2$	$=$ $=$	$- 5$ $-5$ $- 2$ $-2$	$2 - 2$ $2-2$ cancels out
$- 4 x$ $-4x$	$=$ $=$	$- 7$ $-7$

$- 4 x$ $-4x$ $\div (- 4)$ $divide(-4)$	$=$ $=$	$- 7$ $-7$ $\div (- 4)$ $divide(-4)$
$=$ $=$	$- 7$ $-7$ $\div (- 4)$ $divide(-4)$	$\times (- 4) \div (- 4)$ $times(-4)divide(-4)$ cancels out

$x$	$=$	$7/4$

$frac{x+3}{6}-frac{x-1}{5}$	$=$	$1/3$

$frac{x+3}{6}$ $timesfrac{5}{5}$ $-frac{x-1}{5}$ $timesfrac{6}{6}$	$=$	$1/3$ $timesfrac{10}{10}$

$frac{5(x+3)}{30}-frac{6(x-1)}{30}$	$=$	$10/30$

$(5(x+3))/30-(6(x-1))/30$	$=$	$10/30$

$(5(x+3))/30$	$=$	$((x xx5)+(3xx5))/30$

	$=$	$(5x+15)/30$

$(6(x-1))/30$	$=$	$((x xx 6)-(1xx6))/30$

	$=$	$(6x-6)/30$



$(5x+15)/30$ $-$ $(6x-6)/30$	$=$	$10/30$

$frac{(5x+15)-(6x-6)}{30}$	$=$	$10/30$

$frac{-x+21}{30}$	$=$	$10/30$	Combine like terms

$frac{-x+21}{30}$ $times30$	$=$	$10/30$ $times30$	Multiply both sides by $30$

$frac{30(-x+21)}{30}$	$=$	$(30(10))/30$

$-x+21$	$=$	$10$	The coefficient $frac{30}{30}$ cancels out on both sides
$-x+21$ $-21$	$=$	$10$ $-21$	Subtract $21$ from both sides
$-x$ $+21$ $-21$	$=$	$10$ $-21$	$21-21$ cancels out
$-x$	$=$	$-11$

$(-x)/-1$	$=$	$(-11)/-1$	Divide both sides by $-1$

$x$	$=$	$11$