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
Solving Inequalities Part 1 Practice Test:

#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:

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

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

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

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#5:

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

$$a)\hspace{.1em}{-}15 ≥ 15k$$

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

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Written Solutions:

#1:

Solutions:

a) x ≥ 6 : [6,∞) solution x is greater than or equal to 6

b) x ≤ 2 : (-∞,2] solution x is less than or equal to 2

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#2:

Solutions:

a) x ≥ 0 : [0,∞) solution x is greater than or equal to 0

b) k ≥ 19 : [19,∞) solution k is greater than or equal to 19

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#3:

Solutions:

a) n > 3 : (3,∞) solution n is greater than 3

b) v > 4 : (4,∞) solution v is greater than 4

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#4:

Solutions:

a) p > -32 : (-32,∞) solution p is greater than -32

b) x < -40 : (-∞,-40) solution x is less than -40

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#5:

Solutions:

a) k ≤ -1 : (-∞,-1] solution k is less than -1

b) z > 7 : (7,∞) solution z is greater than 7

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