Solve for X in the Fraction Equation: (8x-4)/5 = (2x+2)/4

Question

Solve for x:

$\frac{8x-4}{5}=\frac{2x+2}{4}$

00:00 Solve

00:03 We want to isolate the unknown X

00:07 We'll multiply by both denominators to eliminate fractions

00:16 We'll properly open parentheses, multiply by each factor

00:28 We'll arrange the equation so that one side has only the unknown X

00:50 We'll isolate the unknown X

00:58 And this is the solution to the problem

To get rid of the fraction mechanics, we will cross multiply between the sides:

$4(8x-4)=5(2x+2)$

We expand the parentheses by multiplying the outer element by each of the elements inside the parentheses:

$32x-16=10x+10$

We arrange the sides accordingly so that the elements with the X are on the left side and those without the X are on the right side:

$32x-10x=10+16$

We calculate the elements:

$22x=26$

We divide the two sections by 22:

$\frac{22x}{22}=\frac{26}{22}$

$x=\frac{26}{22}$

$\frac{26}{22}$