Graphing One Variable Two Step Inequalities

Graphing One Variable Two Step Inequalities

by Bryan Foster

Solving One-Step Inequalities

• Isolate the variable

• Use inverse operations to help you isolate the variable

Graphing Inequalities

• < and > have open circles

• ≤ and ≥ have closed circles

x - 5 ≤ 3

• Since the operation in the inequality is subtraction, we will use addition to solve.

• Add 5 to both sides on the inequality sign.

• 5 +3=8

• x≤8

• If we were to graph this, the circle would be closed!

x + 4 ≥9

• Since the operation in the inequality is addition, we will use subtraction to solve.

• Subtract 4 from both sides on the inequality sign.

• 9-4=5

• x≥5

• If we were to graph this, the circle would be closed!

6x ≤ 18

• Since the operation in the inequality is multiplication, we will use division to solve.

• Divide both sides of the inequality sign by 6

• 18 divided by 6 equals 3

• x≤3

• If we were to graph this, the circle would be closed!

• Since the operation in the inequality is division, we will use multiplication to solve.

• Multiply both sides of the inequality sign by 5.

• 4 times 5=20

• x>20

• If we were to graph this, the circle would be open!

Multiple Choice

When graphing b < 6 would you use an open or closed circle?

• Open
• closed

Multiple Choice

What does this symbol represent?

• less than
• greater than
• less than or equal to
• greater than or equal to

Multiple Choice

What does this symbol represent?

• less than
• greater than
• less than or equal to
• greater than or equal to

Multiple Choice

Pick the correct inequality.

• A
• B
• C
• D

Multiple Choice

What are two solutions to x < 8?

• 8.6, 7.9
• 11, 16
• 0.8, 5.9
• 12, 7.1

Multiple Choice

• 3

• 5

• -4.5

• 4.5

Multiple Choice

Match the graph with its inequality.

• 11 < a
• 11 > a
•  11 ≤ a
•  11 ≥ a

Multiple Choice

10 < 3x + 19

• x < 3
• x > 3
• x < -3
• x > -3

Multiple Choice

-8b - 8 > 56 

• b > 6
• b < -8
• b > -8
• b > 7/2

Multiple Choice

Which graph matches the inequality

r ≥ -6?

• A

• B

• C

• D

Multiple Choice

Graph the solution set of the inequality.

–4n + 1 > –23

Multiple Choice

Graph the solution set of the inequality.

2n + 4 < 16

Multiple Choice

$$2\ +\ 6n\ \le\ 4n$$  Solve and graph the inequality.

Multiple Choice

$$8\ +\ 3n\ <\ 53$$  Solve the inequality. 

• $$n\ >\ -21$$  

• $$n\ <\ 15$$  

• $$n\ <\ -\ 21$$  

• $$n\ >\ 15$$  

Multiple Choice

Solve the inequality