Home > CCG > Chapter 5 > Lesson 5.3.1 > Problem5-81

5-81.

Solve the equations below, if possible. If there is no solution, explain why.

1. $\frac { 8 - x } { x } = \frac { 3 } { 2 }$

Multiply both sides by $2x$.

$2x\left(\frac{8-x}{x}\right)=\left(\frac{3}{2}\right)2x$

Distribute the $2$ to both terms and simplify the right side.

$8(2)-x(2)=3x$

Combine like terms on one side.
$16=5x$

$x=\frac{16}{5}$

1. $- 2 ( 5 x - 1 ) - 3 = - 10 x$

Distribute the $-2$ and then simplify before solving for $x$.

1. $x ^ { 2 } + 8 x - 33 = 0$

Factor this equation to find the solutions.

$x=−11$ or $3$

1. $\frac { 2 } { 3 } x - 12 = 180$

Multiply each term by $3$ to simplify.