Solving One-Step Algebraic Inequalities

Solving and Graphing One-Step Inequalities

​Which way?

​When the variable is on the left, the "point" of the inequality sign points the same way that you should draw your line.

​> and > point to the right

​

​< and < point to the left

Multiple Choice

What inequality does the number line graph represent?

• x ≤ 4
• x ≥ -4
• x < -4
• x < 4

Multiple Choice

What inequality does the number line graph represent?

• x ≥ 3
• x > 3
• x < -3
• x ≤ 3

Multiple Choice

Match the graph with its inequality.

• b > –2
• b < –2
• b ≥ –2
• b ≤ –2

Multiple Choice

• x ≠ 0
• x < 0
• x > 0
• x ≤ 0

​Example 1

​1. Subtract 3 from both sides

​2. Open circle at 1

​3. Arrow to the right

​Example 2

​1. Add 3 to both sides

​2. Switch so the variable is on

​ the left side

​3. Closed circle at 3

​4. Arrow to the left

Multiple Choice

Solve

x + 5 > 7

• x > -2
• x > 2
• x > 12
• x > -12

Multiple Choice

Solve

r - 14 ≥ 17

• r ≥ 3
• r ≥ -31
• r ≥ 31
• r ≥ -3

Multiple Choice

Solve

h - 2.7 ≤ 7

• h ≥ -3.4

• h ≥ -9.7

• h ≤ 9.7

• h ≤ 3.4

Multiple Choice

Solve

y - 13 ≤ -15

• y ≤ 2
• y ≤ -2
• y ≤ 28
• y ≤ -28

Multiple Choice

5 < x is the same as

• x > 5

• x < 5

Multiple Choice

Solve

24 ≤ h + 15

• h ≥ -9
• h ≥ 9
• h ≤ 9
• h ≤ 39

​Example 3

​1. Divide both sides by 6

​2. Open circle at -4

​3. Arrow to the left

​Example 4

​1. Divide both sides by -5

2. Flip the inequality sign!!!​

3. Closed circle at 2

​4. Arrow to the left

Multiple Choice

Solve

7n > 49

• n > 7
• n < 7
• n > 343
• n < 343

Multiple Choice

Solve

12 ≥ 6w

• w > 2
• w < 2
• w ≥ 2
• w ≤ 2

Multiple Choice

Solve

-8x < 48

• x < -6

• x > -6

• x < 6

• x > 6

Multiple Choice

Solve 
-9h > -63

• h < 7
• h > 7
• h < -7
• h > -7

Multiple Choice

Solve

1.8m ≥ -5.4

• m ≥ -3
• m ≤ -3
• m ≥ -9.72
• m ≤ -9.72

Open Ended

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