solve the following equation. 2/3 x + 6 = 1/2x + 1/4x A. 6 B. 72 C. 14 2/5 D. 2

Question

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

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

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Sapo 4 days 2021-07-20T04:52:37+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-07-20T04:53:48+00:00

    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 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

     \frac{1}{2} x +  \frac{1}{4} x =  \frac{2}{3} x + 6

    First, Simply each term

    Combine {\frac{1}{2}}, {\frac{1}{4}} to x

     \frac{x}{2}  +  \frac{x}{4}  =  \frac{2}{3} x + 6

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

     \frac{x}{2}  \times  \frac{2}{2}  +  \frac{x}{4}  =  \frac{2}{3} x + 6

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

    Multiply {\frac{x}{2}} and {\frac{2}{2}}

     \frac{x \times 2}{2 \times 2}  +  \frac{x}{4}  =  \frac{2}{3} x + 6

    Multiply 2 and 2

     \frac{x \times 2}{4}  +  \frac{x}{4}  =  \frac{2}{3} x + 6

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

     \frac{x \times 2 + x}{4}  =  \frac{2}{3} x + 6

    Third, Simplify the numerator

    Move 2 to the left of x

     \frac{2 \times x + x}{4}  =  \frac{2}{3} x + 6

    Add 2x and x

     \frac{3x}{4}  =  \frac{2}{3} x + 6

    \blue{\boxed{Note:}} Combine {\frac{2}{3}} and x

     \frac{3x}{4}  =  \frac{2x}{3}  + 6

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

    Subtract {\frac{2x}{3}} from both sides of the equation

     \frac{3x}{4}  -  \frac{2x}{3}  = 6

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

     \frac{3x}{4}  \times  \frac{3}{3}  -  \frac{2x}{3}  = 6

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

     \frac{3x}{4}  \times  \frac{3}{3}  -  \frac{2x}{3}  \times  \frac{4}{4}  = 6

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

    Multiply {\frac{3x}{4}} and {\frac{3}{3}}

     \frac{3x \times 3}{4 \times 3}  -  \frac{2x}{3}  \times  \frac{4}{4}  = 6

    Multiply 4 and 3

     \frac{3x \times 3}{12}  -  \frac{2x}{3}  \times  \frac{4}{4}  = 6

    Multiply {\frac{2x}{3}} and {\frac{4}{4}}

     \frac{3x \times 3}{12}  -  \frac{2x \times 4}{3 \times 4}  = 6

    Multiply 3 and 4

     \frac{3x \times 3}{12}  -  \frac{2x \times 4}{12}  = 6

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

     \frac{3x \times 3 - 2x \times 4}{12}  = 6

    Sixth, Simplify the numerator

    Factor x out of 3x ×3 – 2x × 4

     \frac{x(3 \times 3 - 2 \times 4)}{12}  = 6

    Multiply 3 by 3

     \frac{x(9 - 2 \times 4)}{12}  = 6

    Multiply – 2 by 4

     \frac{x(9 - 8)}{12}  = 6

    Subtract 8 from 9

     \frac{x \times 1}{12}  = 6

    Multiply x by 1

     \frac{x}{12}  = 6

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

    12 \times  \frac{x}{12}  = 12 \times 6

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

    Cancel the common factor

    12 \times  \frac{x}{12}  = 12 \times 6

    Rewrite the expression

    x = 12 \times 6

    Lastly, Multiply 12 by 6

    \blue{\boxed{ x = 72}}

    hope it’s helps

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