# Problem of the Week

## Updated at Nov 14, 2022 3:07 PM

How would you solve the equation $$\frac{x+2}{3}+\frac{4x}{5}=\frac{26}{5}$$?

Below is the solution.

$\frac{x+2}{3}+\frac{4x}{5}=\frac{26}{5}$

 1 Multiply both sides by $$15$$ (the LCM of $$3, 5$$).$5(x+2)+12x=78$2 Expand.$5x+10+12x=78$3 Simplify  $$5x+10+12x$$  to  $$17x+10$$.$17x+10=78$4 Subtract $$10$$ from both sides.$17x=78-10$5 Simplify  $$78-10$$  to  $$68$$.$17x=68$6 Divide both sides by $$17$$.$x=\frac{68}{17}$7 Simplify  $$\frac{68}{17}$$  to  $$4$$.$x=4$Donex=4