# Inequalities, Intervals: Problems with Solutions

By Prof. Hernando Guzman Jaimes (University of Zulia - Maracaibo, Venezuela)
Problem 1
Which the following intervals is the solution to
$-5 < x \leq 3$
Problem 2
Which of the following set of numbers belongs to the interval
$\left[ 7,9\right]$
Problem 3
Solve the inequality
$2x+3>-2$
Problem 4
What is the solution to the inequality?
$3x-9<6$
Problem 5
Write the solution in interval notation and graph it on the real number line.
$\frac{3}{2}x+4\leq 10$
Problem 6
Write the solution in interval notation and graph it on the real number line.
$5-\frac{5}{2}x\geq -4$
Problem 7
Write the solution in interval notation and graph it on the real number line.
$\frac{5}{2}-x>x$
Problem 8
Select the solution in interval notation and graph it on the real number line.
$-\left( 1-x\right) \geq 2x-1$
Problem 9
$2+x\geq 3\left( x-1\right)$
Problem 10
Solve the inequality:
$-7x+3\leq 4-x$

Problem 11
$-7\leq -x<2$
Problem 12
Solve and graph the compound inequality.
$-\frac{20}{3}< \frac{2}{3}x < x$
Problem 13
Solve and graph the compound inequality.
$-7 < x-2 < 1$
Problem 14
Solve and graph the compound inequality.
$3 < x-4\leq 10$
Problem 15
Solve and graph the compound inequality.
$-1 < \frac{x-4}{4}\leq \frac{1}{2}$
Problem 16
Solve and graph the compound inequality.
$2\leq \frac{4x+2}{3}\leq 10$
Problem 17
Solve the absolute-value inequality:
$\left\vert x-4\right\vert \leq 9$
Problem 18
Solve the absolute-value inequality:
$\left\vert 2x-7\right\vert \leq 1$
Problem 19
Solve the absolute-value inequality:
$\left\vert x+\sqrt{2}\right\vert \geq 1$
Problem 20
Solve the absolute-value inequality:

$\left\vert \frac{3x-1}{-4}\right\vert <2$
Problem 21
Solve the absolute-value inequality:
$\left\vert \frac{3-5x}{3}\right\vert \geq 5$

Correct:
Wrong:
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