If \frac{20}{x - 3} = 4, what is the value of x + 2? — SAT

If $\frac{20}{x - 3} = 4$ , what is the value of $x + 2$ ?

Answer: 10

To solve the equation

\frac{20}{x - 3} = 4

, multiply both sides by

x - 3

to get

20 = 4(x - 3)

. Distributing the 4 gives

20 = 4x - 12

. Adding 12 to both sides yields

32 = 4x

, and dividing by 4 gives

x = 8

. Substituting

x = 8

into the expression

x + 2

gives

8 + 2 = 10

Multiply both sides of the equation by the denominator

x - 3

20 = 4(x - 3)

To eliminate the fraction and rewrite the rational equation in linear form.

Distribute the constant on the right side of the equation.

20 = 4x - 12

To remove the parentheses by multiplying 4 by both

x

and

-3

Add 12 to both sides of the equation.

32 = 4x

To isolate the term with the variable

x

on one side of the equation.

Divide both sides of the equation by 4.

x = 8

To solve for the variable

x

Substitute the value of

x

into the expression

x + 2

10

The question asks for the value of the expression

x + 2

rather than just the variable

x

Solving rational equations by clearing the denominator and isolating the variable to evaluate algebraic expressions.

Question