About Linear Inequalities in one Variable:

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
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)


#2:

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

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


#3:

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

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


#4:

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

a) -28 ≤ 4n - 8 ≤ -20


#5:

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

a) -49 ≤ -9a + 5 ≤ - 4


Written Solutions:

#1:

Solutions:

a) n > 0

(0, ∞)

graphing an interval on a number line


#2:

Solutions:

a) n > 9

(9, ∞)

graphing an interval on a number line


#3:

Solutions:

a) $$n > \frac{3}{2}$$

$$\left(\frac{3}{2},∞\right)$$

graphing an interval on a number line


#4:

Solutions:

a) -5 ≤ n ≤ -3

[-5,-3]

graphing an interval on a number line


#5:

Solutions:

a) 1 ≤ a ≤ 6

[1,6]

graphing an interval on a number line