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Solve the following equation. 2/3 x + 6 = 1/2x + 1/4x

A. 6
B. 72
C. 14 2/5
D. 2

1 Answer

1 vote

QUESTION:

Solve the following equation 2/3 x + 6 = 1/2 x + 1/4x

ANSWER:

In all choices the correct answer is B
\blue{\boxed{72}}

STEP-BY-STEP Step-by-step explanation:


\blue{\boxed{Note:}} Since x is on the right side of the equation, switch the sides so it is on the left side of the equation


(1)/(2) x + (1)/(4) x = (2)/(3) x + 6

First, Simply each term

Combine
{(1)/(2)},
{(1)/(4)} to x


(x)/(2) + (x)/(4) = (2)/(3) x + 6


\blue{\boxed{Note:}} To write
{(x)/(2)} as a fraction with a common denominator, multiply by
{(2)/(2)}


(x)/(2) * (2)/(2) + (x)/(4) = (2)/(3) x + 6

Second, Write each expression with a common denominator of 4, by multiplying each by appropriate factor of 1

Multiply
{(x)/(2)} and
{(2)/(2)}


(x * 2)/(2 * 2) + (x)/(4) = (2)/(3) x + 6

Multiply 2 and 2


(x * 2)/(4) + (x)/(4) = (2)/(3) x + 6


\blue{\boxed{Note:}} Combine the numerators over the common denominator


(x * 2 + x)/(4) = (2)/(3) x + 6

Third, Simplify the numerator

Move 2 to the left of x


(2 * x + x)/(4) = (2)/(3) x + 6

Add 2x and x


(3x)/(4) = (2)/(3) x + 6


\blue{\boxed{Note:}} Combine
{(2)/(3)} and x


(3x)/(4) = (2x)/(3) + 6

Fourth, Move all terms containing x to the left side of the equation

Subtract
{(2x)/(3)} from both sides of the equation


(3x)/(4) - (2x)/(3) = 6


\blue{\boxed{Note:}} To write
{(3x)/(4)} as a fraction with a common denominator, multiply by
{(3)/(3)}


(3x)/(4) * (3)/(3) - (2x)/(3) = 6


\blue{\boxed{Note Again:}} To write
{(-2x)/(3)} as a fraction with a common denominator, multiply by
{(4)/(4)}


(3x)/(4) * (3)/(3) - (2x)/(3) * (4)/(4) = 6

Fifth, Write each expression with a common denominator of 12, by multiplying each by an appropriate factor of 1

Multiply
{(3x)/(4)} and
{(3)/(3)}


(3x * 3)/(4 * 3) - (2x)/(3) * (4)/(4) = 6

Multiply 4 and 3


(3x * 3)/(12) - (2x)/(3) * (4)/(4) = 6

Multiply
{(2x)/(3)} and
{(4)/(4)}


(3x * 3)/(12) - (2x * 4)/(3 * 4) = 6

Multiply 3 and 4


(3x * 3)/(12) - (2x * 4)/(12) = 6


\blue{\boxed{Note:}} Combine the numerators over the common denominator


(3x * 3 - 2x * 4)/(12) = 6

Sixth, Simplify the numerator

Factor x out of 3x ×3 - 2x × 4


(x(3 * 3 - 2 * 4))/(12) = 6

Multiply 3 by 3


(x(9 - 2 * 4))/(12) = 6

Multiply - 2 by 4


(x(9 - 8))/(12) = 6

Subtract 8 from 9


(x * 1)/(12) = 6

Multiply x by 1


(x)/(12) = 6


\blue{\boxed{Note:}} Multiply both sides of the equation by 12


12 * (x)/(12) = 12 * 6

Seventh, Simplify both sides of the equation and cancel the common factor of 12

Cancel the common factor


12 * (x)/(12) = 12 * 6

Rewrite the expression


x = 12 * 6

Lastly, Multiply 12 by 6


\blue{\boxed{ x = 72}}

hope it's helps

User Argoneus
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