Key to "Solve: x+34=x−23+14."

Chaya Galloway

Answered question

2021-09-16

Solve:

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

Answer & Explanation

diskusje5

Skilled2021-09-17Added 82 answers

Fractions in an equation can be removed by multiplying the equation by the least common denominator. The least common denominator is determined by looking at all the denominators and finding their least common multiple.
A linear equation in a variable x can be solved by moving the constant terms to one side and moving the variable terms to one side. Then finally divide both sides by coefficient of the variable term.
Denominators are 3,4,4. Least common denominator is 12. Multiply the given equation by 12 to remove the fractions from the given equation.

12 \frac{x + 3}{4} = 12 \frac{x - 2}{3} + 12 \frac{1}{4}

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

3 x + 9 = 4 x - 8 + 3

3 x + 9 = 4 x - 5

3 x + 9 - 3 x = 4 x - 5 - 3 x

9 = x - 5

9 + 5 = x - 5 + 5

x = 14

Hence, solution to given equation is

x = 14

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Pre-Algebra

Didn't find what you were looking for?