Checkpoint: Solving Square Root Inequalities Solution

Solve. Graph the solution on a number line.

$- 6 + \sqrt{9 - 5 x} \geq 2$

Restrictions

$\begin{matrix} 9 - 5 x \geq 0 \\ 9 \geq 5 x \\ x \leq \frac{9}{5} \end{matrix}$

Solve

$\begin{matrix} \sqrt{9 - 5 x} \geq 8 \\ {(\sqrt{9 - 5 x})}^{2} \geq {(8)}^{2} \\ 9 - 5 x \geq 64 \\ - 5 x \geq 55 \\ x \leq - 11 \end{matrix}$

Note

Remember that when you multiply or divide an inequality by a negative number, the direction of the inequality symbol changes.

Remember to compare the radicand inequalities to the inequality solution to determine which combination of the results produces the most restrictive answer. Any result that is found outside of the most restricted combination is extraneous.

Q: How can you determine if the solution is correct?

A: Substitute 3 numbers (lower, higher, and the same value), and see if any value makes the given inequality true.