Solve Equations with Variables on Both Sides using the Distributive Property 4

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Question 1 of 5

Solve for

$a$

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

$a=$ (3)

Question 2 of 5

Solve for

$x$

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

$x=$ (-9)

Question 3 of 5

Solve for

$n$

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

$n=$ (10)

Question 4 of 5

Solve for

$x$

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

$x=$ (7/4)

Question 5 of 5

Solve for

$x$

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

$x=$ (11)

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

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

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

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

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

Solve Equations with Variables on Both Sides using the Distributive Property 4

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Quiz summary

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2. Question

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3. Question

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4. Question

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5. Question

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Quizzes

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

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

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

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

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

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

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

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

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

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

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

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

$-4x$ $divide(-4)$	$=$	$-7$ $divide(-4)$
$=$	$-7$ $divide(-4)$	$times(-4)divide(-4)$ 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 $-1$

$x$	$=$	$11$