Solving a linear inequality in one variable is similar to solving a linear equation in one variable. Our goal is still to isolate the variable on one side, with a number on the other side. We must always remember to flip the inequality symbol when multiplying or dividing by a negative number.

Test Objectives
• Demonstrate the ability to use the addition property of inequality
• Demonstrate the ability to use the multiplication property of inequality
• Demonstrate the ability to solve a linear inequality in one variable
Solving Linear Inequalities Practice Test:

#1:

Instructions: solve each inequality, write in interval notation, graph.

$$a)\hspace{.2em}315 ≥ -5(1 - 8x)$$

$$b)\hspace{.2em}{-}133 > 7(2x - 3)$$

#2:

Instructions: solve each inequality, write in interval notation, graph.

$$a)\hspace{.2em}{-}106 < -2(7x - 3)$$

$$b)\hspace{.2em}\frac{309}{56}+ 6x ≥ -\frac{6}{7}x - \frac{1}{2}x$$

#3:

Instructions: solve each inequality, write in interval notation, graph.

$$a)\hspace{.2em}\frac{367}{168}+ x + \frac{1}{3}+ \frac{7}{8}x ≥ \frac{1}{3}x + \frac{13}{7}$$

$$b)\hspace{.2em}4(x + 5) - 5 ≥ -(3x - 3) + 5$$

#4:

Instructions: solve each inequality, write in interval notation, graph.

$$a)\hspace{.2em}4(x - 1) ≤ -2(x + 5)$$

$$b)\hspace{.2em}5(x - 1) < 4(x - 4) + 2$$

#5:

Instructions: solve each inequality, write in interval notation, graph.

$$a)\hspace{.2em}4(x + 1) - 2(x + 2) > -5x - 3x$$

$$b)\hspace{.2em}x - 4(3x + 3) ≤ 4(-3x - 3) + 4x$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}x ≤ 8, (-\infty, 8]$$ $$b)\hspace{.2em}x < -8, (-\infty, -8)$$ #2:

Solutions:

$$a)\hspace{.2em}x < 8, (-\infty, 8)$$ $$b)\hspace{.2em}x ≥ -\frac{3}{4}, \left[-\frac{3}{4}, \infty\right)$$ #3:

Solutions:

$$a)\hspace{.2em}x ≥ -\frac{3}{7}, \left[-\frac{3}{7}, \infty\right)$$ $$b)\hspace{.2em}x ≥ -1, [-1, \infty)$$ #4:

Solutions:

$$a)\hspace{.2em}x ≤ -1, (-\infty, -1]$$ $$b)\hspace{.2em}x < -9, (-\infty, -9)$$ #5:

Solutions:

$$a)\hspace{.2em}x > 0, (0, \infty)$$ $$b)\hspace{.2em}x ≥ 0, [0, \infty)$$ 