Question

Solve$7=\frac{1}{2}x+\frac{3}{4}x-\frac{2}{3}x$

Short answer

The answer is$x=12$

Step-by-step solution

Step 1. Given information

The equation is $7=\frac{1}{2}x+\frac{3}{4}x-\frac{2}{3}x$

Find value of x.

Step 2. Calculation

Find LCD of denominators of equation $7=\frac{1}{2}x+\frac{3}{4}x-\frac{2}{3}x$

LCD of 2,3,4 is 12

So

$7\times 12=12\left(\frac{1}{2}x+\frac{3}{4}x-\frac{2}{3}x\right)$

role="math" localid="1644248969105" $84=6x+9x-8x$

Combine like terms

role="math" localid="1644249012482" $$\begin{gathered} 84=7x \\ \frac{84}{7}=x \\ 12=x \end{gathered}$$