Example 1 :
Solve the inequality given below. Graph and check the solution.
x + 5 < -12
Solution :
Step 1 :
Solve the inequality
x + 5 < -12
Use the Subtraction Property of Inequality.
Subtract 5 on from both sides.
(x + 5) - 5 < -12 - 5
x < -17
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 -18 for x into x + 5 < -12.
-18 + 5 < -12
-13 < -12
The inequality is true.
Example 2 :
Solve the inequality given below. Graph and check the solution.
8 ≤ y - 3
Solution :
Step 1 :
Solve the inequality
8 ≤ y - 3
Use the Addition Property of Inequality.
Add 3 to to both sides.
8 + 3 ≤ (y - 3) + 3
11 ≤ y
or y ≥ 11
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 12 for y into 8 ≤ y - 3.
8 ≤ 12 - 3
8 ≤ 9
The inequality is true.
Example 3 :
Solve the inequality given below. Graph and check the solution.
x + 3 < 8
Solution :
Step 1 :
Solve the inequality
x + 3 < 8
Use the Subtraction Property of Inequality.
Subtract 3 from both sides.
(x + 3) - 3 < 8 - 3
x < 5
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 0 for x into x + 3 < 8.
0 + 3 < 8
3 < 8
The inequality is true.
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