### About Solving Linear Inequalities Part 1:

When we solve a linear inequality in one variable we turn to a few new properties. We utilize the addition property of inequality, along with the multiplication property of inequality. These two properties allow us to isolate our variable on one side of the inequality.

Test Objectives

- Demonstrate the ability to solve a linear inequality
- Demonstrate an understanding of interval notation
- Demonstrate the ability to graph an interval using a number line

#1:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

$$a)\hspace{.1em}x - 1 ≥ 5$$

$$b)\hspace{.1em}{-}20 + x ≤ -18$$

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#2:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

$$a)\hspace{.1em}{-}17 ≤ x - 17$$

$$b)\hspace{.1em}k + 19 ≥ 38$$

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#3:

Instructions: Solve each inequality, write the answer in interval notation, and graph each interval on the number line.

$$a)\hspace{.1em}\frac{3}{14}< \frac{n}{14}$$

$$b)\hspace{.1em}{-}15v < -60$$

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#4:

$$a)\hspace{.1em}\frac{p}{8}> -4 $$

$$b)\hspace{.1em}{-}5 > \frac{x}{8}$$

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#5:

$$a)\hspace{.1em}{-}15 ≥ 15k$$

$$b)\hspace{.1em}{-}2z < -14$$

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Written Solutions:

#1:

Solutions:

a) x ≥ 6 : [6,∞)

b) x ≤ 2 : (-∞,2]

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#2:

Solutions:

a) x ≥ 0 : [0,∞)

b) k ≥ 19 : [19,∞)

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#3:

Solutions:

a) n > 3 : (3,∞)

b) v > 4 : (4,∞)

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#4:

Solutions:

a) p > -32 : (-32,∞)

b) x < -40 : (-∞,-40)

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#5:

Solutions:

a) k ≤ -1 : (-∞,-1]

b) z > 7 : (7,∞)