Example 1 :
Solve the inequality given below. Graph and check the solution.
y/3 ≥ 5
Solution :
Step 1 :
Solve the inequality
y/3 ≥ 5
Use the Multiplication Property of Inequality.
Multiply both sides by 3.
3.(y/3) ≥ (5).3
y ≥ 15
Step 2 :
Graph the solution.
Step 3 :
Check the solution by substituting a solution from the shaded part of the graph into the original inequality. For convenience, choose a multiple of 3.
Substitute 18 for x into y/3 ≥ 5
18/3 ≥ 5
6 ≥ 5
The inequality is true.
Example 2 :
Solve the inequality given below. Graph and check the solution.
-4x > 52
Solution :
Step 1 :
Solve the inequality
-4x > 52
Use the Division Property of Inequality.
Divide both sides by -4.
(-4x) / (-4) < 52 / (-4)
x < -13
Step 2 :
Graph the solution.
Step 3 :
Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.
Substitute -15 for x into -4x > 52.
-4.(-15) > 52
60 > 52
The inequality is true.
Example 3 :
Solve the inequality given below. Graph and check the solution.
-10y < 60
Solution :
Step 1 :
Solve the inequality
-10y < 60
Use the Division Property of Inequality.
Divide both sides by -10.
(-10y) / (-10) > 60 / (-10)
y > -6
Step 2 :
Graph the solution.
Step 3 :
Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.
Substitute -2 for y into -10y < 60.
(-10).(-2) < 60
20 < 60
The inequality is true.
Example 4 :
Solve the inequality given below. Graph and check the solution.
7 ≥ -t/6
Solution :
Step 1 :
Solve the inequality
7 ≥ -t/6
Use the Multiplication Property of Inequality.
Multiply both sides by -6.
7.(-6) ≤ (-t/6).(-6)
-42 ≤ t
or t ≥ -42
Step 2 :
Graph the solution.
Step 3 :
Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.
Substitute -40 for t into 7 ≥ -t/6.
7 ≥ -(-40)/6
7 ≥ 20/3
7 ≥ 6.67
The inequality is true.
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