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 in one Variable 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:
Solution:
a) n > 0
(0, ∞)
Solution:
a) n > 9
(9, ∞)
Solution:
a) $$n > \frac{3}{2}$$
$$\left(\frac{3}{2},∞\right)$$
Solution:
a) -5 ≤ n ≤ -3
[-5,-3]
Solution:
a) 1 ≤ a ≤ 6
[1,6]