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Equation with Fractions - Algebra

by Kim
(Atlanta, GA, USA)










































Solve the equation (1/2)x + 2/3 =3/4 by first clearing all the fractions, then solving for x. Please show work and explain every step. Leave your answer as a fraction.

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Mar 29, 2012
Equation with Fractions
by: Staff


Question:

by Kim
(Atlanta, GA, USA)


Solve the equation (1/2)x + 2/3 =3/4 by first clearing all the fractions, then solving for x. Please show work and explain every step. Leave your answer as a fraction.



Answer:

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


Subtract 2/3 from each side of the equation to remove the 2/3 from the left side of the equation.

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

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

(1/2)x + 0 = 3/4 - 2/3

(1/2)x = 3/4 - 2/3


Subtract the second fraction from the first fraction on the right side of the equation.

(1/2)x =(3/4)*(3/3) - (2/3)*(4/4)

(1/2)x =(3*3)/(4*3) - (2*4)/(3*4)

(1/2)x =(9)/(12) - (8)/(12)

(1/2)x =(9 - 8)/(12)

(1/2)x =(1/12)


Multiply both sides of the equation by (2/1). This will remove the (1/2) from the left side of the equation. (2/1) is the reciprocal of the fraction (1/2).

(2/1) * (1/2)x = (2/1) * (1/12)

(2*1)/(1*2)x = (2/1) * (1/12)

(2/2)*(1/1)*x = (2/1) * (1/12)

(1)*(1)*x = (2/1) * (1/12)

x = (2/1) * (1/12)

x = (2*1)/(1*12)

x = (2)/(12)


Reduce the fraction 2/12 to its lowest terms. l

x = 2/12

x = (2*1)/(2*6)

x = (2/2) * (1/6)

x = (1) * (1/6)

x = 1/6

x = 0.166667


>>> the final answer: x = 1/6 or x = 0.166667


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Check the solution by substituting 1/6 for the “x” in the original equation

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

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

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

1/12 + 2/3 =3/4

1/12 + (2/3)*(4/4) =3/4

1/12 + (2*4)/(3*4) =3/4

1/12 + (8)/(12) =3/4

1/12 + 8/12 =3/4

(1 + 8)/12 =3/4

9/12 =3/4

(3*3)/(3*4) =3/4

(3/3) * (3/4) =3/4

(1) * (3/4) =3/4

(3/4) =3/4

3/4 =3/4, OK → x = 1/6 is a valid solution





Thanks for writing.

Staff
www.solving-math-problems.com



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