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.

Comments for Equation with Fractions - Algebra

 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 --------------------------------------- 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