If \frac{8}{x - 3} = 2, what is the value of x? — SAT

If $\frac{8}{x - 3} = 2$ , what is the value of $x$ ?

Answer: 7

To solve the equation

\frac{8}{x - 3} = 2

, we clear the denominator by multiplying both sides of the equation by

x - 3

. This gives

8 = 2(x - 3)

. Distributing the

2

results in

8 = 2x - 6

. Adding

6

to both sides yields

14 = 2x

. Dividing both sides by

2

gives the solution

x = 7

Multiply both sides of the equation by

x - 3

to eliminate the fraction.

8 = 2(x - 3)

To clear the denominator and simplify the equation.

Distribute the 2 to the terms inside the parentheses.

8 = 2x - 6

To expand the right-hand side of the equation.

Add 6 to both sides of the equation.

14 = 2x

To isolate the term with the variable

x

Divide both sides by 2 to solve for

x

x = 7

To find the final value of the variable.

Solving a rational equation that simplifies to a linear equation by multiplying by the common denominator.

Question