Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

2(x+13)=(x−2)⋅8

Solve the equation for x.

Simplify 2(x+13).

Start simplifying.

0+0+2(x+13)=(x−2)⋅8

Simplify by adding zeros.

2(x+13)=(x−2)⋅8

Apply the distributive property.

2x+2⋅13=(x−2)⋅8

Multiply 2 by 13

2x+26=(x−2)⋅8

Simplify (x−2)⋅8

Apply the distributive property.

2x+26=x⋅8−2⋅8

Simplify the expression.

Move 8 to the left of x

2x+26=8⋅x−2⋅8

Multiply −2 by 8

2x+26=8x−16

Move all terms containing x to the left side of the equation.

Subtract 8x from both sides of the equation

2x+26−8x=−16

Subtract 8x from 2x

−6x+26=−16

Move all terms not containing x to the right side of the equation.

Subtract 26 from both sides of the equation

−6x=−16−26

Subtract 26 from −16

−6x=−42

Divide each term in −6x=−42 by −6 and simplify

Divide each term in −6x=−42 by −6

Simplify the left side

Cancel the common factor of −6.

Divide x by 1.

Simplify the right side.

Divide −42 by −6.

x=7

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3 years ago