Download Solving Inequalities

Solving Inequalities
To solve an inequality you follow the same steps as solving an equation.
Step 1 is to ungroup or distribute
Step 2 is to remove all fractions by multiplying every term by the LCD
Step 3 is to combine like terms on each side of the equation or inequality
Step 4 is to isolate the variable
Step 5 is to do the opposite operation until you get the variable by itself
The only difference is when you divide or multiply by a negative number in
Step 5 you reverse the direction of the inequality.
Example
-2X + 6 > 2
-6 -6
-2X > -4
-2X/-2 < -4/-2
X<2
Example
4X + 8  8X + 12
-8X
-8X
-4X + 8  12
- 8 -8
-4X  4
-4X/-4  4/-4
X  -1
Example
3X + 5 > 2X + 8
-2X
-2X
X+5>8
-5 -5
X>3
Example
2(3X -5) < 4X – 6
6X – 10 < 4X – 6
-4X
-4X
2X – 10 < - 6
+ 10 + 10
2X < 4
2X/2 < 4/2
X<2
Solve the following inequalities
1)
5X – 2 > 3X + 6
3) -12X > 36
2) 6X – 9  4X – 11
4) 5X – 6 < 9
5) 22  8X + 6
6) 5X – 4 + 3X > 6X + 15
7) 4X – 3 – 2X  12X + 8
8) 3(2X – 7) > 8X + 12
9) 3(3X – 5) + 4X  5X – 5 + 2X
10)
2X  7
10
X 3
+
<
4
6
2
12) 5X – 3(2X + 5) > 8X – 14 – 3X
11)
8  4X
X 2
+
 2X + 5
3
5
13) 6X + 5 – 12X + 4  7(4 – 2X) + 9
14) Write the inequality that shows 4 more than 3 times a number is greater than
12.
15) Write the inequality that shows 6 less than twice a number is less than or equal
to 22.
16) Write the inequality that shows the sum of two different numbers is the same
or greater than 55.
17) Write the inequality that shows 4 less than five times a number is less than 36
added to the same number.