Solve each absolute value equation.

$$a. \left| x ^ { 2 } - 3 x - 14 \right| = 4 \quad b. x ^ { 2 } = | x | + 6$$

Express the fact that twice x differs from -1 by more than 5 as an inequality involving absolute value. Solve for x.

True or false? Explain your answer. If we add the absolute values of $-3$ and $-5$, we get $8$ .

Plot the numbers in the same complex plane and find their absolute values.
$\frac3 2-\frac 7 2$i

Write an inequality using an absolute value to describe each statement. x is more than 5 units from 2.

Write each statement using an absolute value equation or inequality. m is no more than 2 units from 7.

If applicable, and properties of absolute value to solve each equation or inequality. $\left|4 x^{2}-23 x-6\right|=0$

Solve each absolute value inequality.

$$1 < \left| x - \frac { 11 } { 3 } \right| + \frac { 7 } { 3 }$$

Solve the absolute value inequality. Graph the solution set and write it using interval notation. |2x + 7| < 3

Write the fact that x differs from 3 by less than $\frac{1}{2}$ as an inequality involving an absolute value.

Solve the absolute value inequality. Express the answer using interval notation and graph the solution set. |x + 6| < 0.001

Solve each absolute value inequality. Graph the solution. $-\frac{1}{3}|f+3|+2 \geq-5$

Solve each absolute value inequality.

$$1 < \left| x - \frac { 11 } { 3 } \right| + \frac { 7 } { 3 }$$

Solve the given absolute value inequality. Graph the solution set and write it in interval notation.

$$|6 x-5| \leq-1$$