About Linear Inequalities in One Variable:

Solving a linear inequality in one variable is very similar to solving a linear equation. The main goal is to get the variable on one side and a number on the other. When encountering a three-part inequality, our goal is to isolate the variable in the middle. It's important to always remember that if we multiply or divide by a negative number, we must flip the direction of all inequality symbols.

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 multi-step linear inequality in one variable
  • Demonstrate the ability to solve a three-part linear inequality in one variable
  • Demonstrate the ability to write an inequality solution in interval notation
  • Demonstrate the ability to graph an interval on the number line
Linear Inequalities in One Variable Practice Test:

#1:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) $$-7(-5 + 4n) < -n - 5(n - 7)$$

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#2:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) $$-3 - 5(2n + 9) < 9(-n - 5) - 12$$

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#3:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) $$2n - \frac{5}{2}n < \frac{5}{3}n - \frac{13}{4}$$

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#4:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) $$-28 ≤ 4n - 8 ≤ -20$$

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#5:

Instructions: Solve each inequality, write the solution in interval notation, and graph the interval.

a) $$-49 ≤ -9a + 5 ≤ - 4$$

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Written Solutions:

#1:

Solutions:

a) $$n > 0$$ $$(0, ∞)$$ graphing an interval on a number line

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#2:

Solutions:

a) $$n > 9$$ $$(9, ∞)$$ graphing an interval on a number line

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#3:

Solutions:

a) $$n > \frac{3}{2}$$ $$\left(\frac{3}{2},∞\right)$$ graphing an interval on a number line

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#4:

Solutions:

a) $$-5 ≤ n ≤ -3$$ $$[-5,-3]$$ graphing an interval on a number line

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#5:

Solutions:

a) $$1 ≤ a ≤ 6$$ $$[1,6]$$ graphing an interval on a number line

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