Question

2.08 - solve linear equations with fractions
due sunday by 11:59pm points 100 submitting an external tool available sep 8
question
solve: $\frac{7}{12}x-\frac{4}{5}x - \frac{1}{3}x=-\frac{1}{4}$.
provide your answer below:
x =

Explanation:

Step1: Find a common - denominator

The common denominator of 12, 5, and 3 is 60. Rewrite the left - hand side of the equation: $\frac{7}{12}x-\frac{4}{5}x - \frac{1}{3}x=\frac{7\times5}{12\times5}x-\frac{4\times12}{5\times12}x-\frac{1\times20}{3\times20}x=\frac{35}{60}x-\frac{48}{60}x-\frac{20}{60}x$.

Step2: Combine like terms

$\frac{35}{60}x-\frac{48}{60}x-\frac{20}{60}x=\frac{35 - 48-20}{60}x=\frac{35-(48 + 20)}{60}x=\frac{35 - 68}{60}x=-\frac{33}{60}x$.
So the equation becomes $-\frac{33}{60}x=-\frac{1}{4}$.

Step3: Solve for x

Multiply both sides of the equation by $-\frac{60}{33}$ to isolate x. $x =-\frac{1}{4}\times(-\frac{60}{33})$.
$x=\frac{60}{4\times33}=\frac{5}{11}$.

Answer:

$x = \frac{5}{11}$