Learning to solve and graph inequalities is easy and straightforward once you know how to solve two-step equations.
Example #1:
Solve x + 3 < 9
x + 3 < 9
Subtract 3 from each side of the equation
x + 3 - 3 < 9 - 3
x + 0 < 6
x < 6
Graph the solution
Check:
Choose a point on the graph such as 4.
4 + 3 = 7 and 7 is smaller than 9
Example #2:
Solve 5x - 2 ≥ 13
5x - 2 ≥ 13
Add 2 to each side of the equation
5x - 2 + 2 ≥ 13 + 2
5x + 0 ≥ 15
5x ≥ 15
Divide each side by 5
5x/5 ≥ 15/5
x ≥ 3
Graph the solution
Notice how this time the circle is shaded at 3 meaning that 3 is included in the solution.
Check:
Choose a point on the graph such as 7.
5(7) - 2 = 35 - 2 = 33 and 33 is bigger than 7.
Example #3:
Solve 2 + 3(5 - x) ≥ 38
2 + 3(5 - x) ≥ 38
Use the distributive property
2 + 15 - 3x ≥ 38
Simplify by adding 2 and 15
17 - 3x ≥ 38
Subtract 17 from each side of the equation
17 - 17 - 3x ≥ 38 - 17
0 - 3x ≥ 21
-3x ≥ 21
Divide each side by -3 and reverse the inequality
-3x/-3 ≤ 21/-3
x ≤ -7
Graph the solution
Check:
Choose a point on the graph such as -10.
2 + 3(5 - -10) = 2 + 3(5 + +10) = 2 + 3(15) = 2 + 45 = 47 and 47 is bigger than 38.
Sep 17, 23 09:46 AM
Jun 09, 23 12:04 PM