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Notes – Multi-Step Inequalities
Tips for Solving Inequalities:
1. Solve inequalities just like an equation…except for the equal sign is an INEQUALity sign instead.
2. If you multiply or divide by a negative to isolate the variable, you must FLIP the sign.
3. Plug in your answer to be sure your sign is correct!
Let’s Try It:
1)
2b  4  6
Step 1: Subtract 4 from both sides
4 4
2b
2
10

2
b5
2)
Step 2: Divide both sides by -2 to get b by itself
We MUST switch the inequality since we divided by a negative number.
6 x  4  2 x  12
2x
2x
Step 1: Get the variable x on one side by subtracting 2x
4 x  4  12
4 4
4x
4

Step 2: Add 4 to both sides
16
Step 3: Divide both sides by 4 to get x by itself
4
x4
3) 3a  2(6a  4)  4  1(a  6)
3a  12a  8  4  4a  6
9a  8  4a  2
4a
4a
Step 1: Distribute
Step 2: Combine like terms (3a-12a = -9a) and (4-6 = -2)
Step 3: Get the variable a on one side by adding 4a
5a  8  2
8
5a
5
8

10
5
a2
Step 4: Subtract 8 from both sides
Step 5: Divide both sides by -5 to get a by itself
We MUST switch the inequality since we divided by a negative number.
Partial Notes from teachers.henrico.k12.va.us
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4)
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x
1  3
2
1 1
(2)
x
2
Step 1: Add 1 to both sides
 4(2)
Step 2: Multiply both sides by 2 to get x by itself
x8
5) 2( y  2)  4  2 y
2 y  4  4  2 y
2y
2y
Step 1: Distribute
Step 2: Subtract 2y from both sides
4  4
Since the variable cancels the answer will be either All Solutions or No Solution. To determine which one we must
determine whether the inequality is true or false; true meaning All Solutions and false meaning No Solution.
Since the inequality 4  4 is true the answer is All Numbers.
6) 2k  17  2(8  k )
2k  17  16  2k
2k
2k
Step 1: Distribute
Step 2: Subtract 2k from both sides
17  16
Since the inequality 17  16 is false the answer is No Solution.
You Try:
1. Solve 5m - 8 > 12.
4. Solve 2r - 18 ≤ 5r + 3.
2. Solve 12 - 3a > 18.
5. Solve 26p - 20 > 14p + 64.
3. Solve 5m - 4 < 2m + 11.
Partial Notes from teachers.henrico.k12.va.us
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Date:
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Partial Notes from teachers.henrico.k12.va.us