  ### Home > AC > Chapter 10 > Lesson 10.3.2 > Problem10-116

10-116.

Solve the following equations and inequalities, if possible. Represent each solution on a number line.

1. $\frac{3}{9}-\frac{x}{3}=\frac{x}{5}$

Multiply the equation by a common multiple of the denominators to remove the fractions.

$45\left(\frac{3}{9}-\frac{x}{3}=\frac{x}{5}\right)$

$15-15x=9x$

Solve for $x$.

$\frac{5}{8} = x$ 1. $\left(3+x\right)^2<9$

Find the boundary point.
$\left(3+x\right)^2=9$

Take the square root of both sides.
$3+x=\pm3$

Solve for $x$.

Test numbers on all sides of the boundary points.

$(3+(-7))^2<9(3+(-1))^2<9(3+(1))^2<9$
$(-4)^2<92^2<94^2<9$
$16<94<916<9$
False True False 1. $8\left|x+1\right|\ge64$

Divide both sides by $8$.

The absolute value of what two numbers equals $8$?

Follow the steps in part (b).

1. $11-\sqrt{x+3}=13$

Subtract $11$ from both sides.

Square both sides.

Subtract $3$ from both sides.

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

Follow the steps in part (a).

A common multiple of $x$ and $8$ is $8x$.

1. $\left|x-5\right|+1>0$

Follow the steps in part (c).