Solving and Graphing Linear Inequalities

See this rule in action

Notice we are multiplying both sides by negative two. Notice how the greater than > symbol changed to a less than symbol <. Keep in mind that the variable can be on either side. X<6 is the same as 6>X. This is read X is less than 6, so generally we want the X on the left side, so be careful to keep the inequality facing the correct way if you change it.

Try some questions...

Use paper and pencil if needed.

Remember solving equations by isolating the variable?

We solve inequalities the same way! There can be one-step or two-step or multi-step depending on how many operations there are. Just remember to isolate the variable by getting the variable on one side of the inequality and everything else to the other side.

Multiple Choice

Does the sign need to flip when solving?
-2x ≥ 22

• YES
• NO

Multiple Choice

Which of the following is the graph of

3x - 2y < 10? note! Solve for y or you can use Desmos to validate your answer.

Multiple Choice

-4x + 14 ≤ 54

• x ≥ - 10

• x ≤ -10

• x ≥ 10

• x ≤ 10

Multiple Choice

Solve for x

3x − 8 ≥ 4(x − 1.5)

• x ≥ 3.5

• x ≤ 3.5

• x ≥ −2

• x ≤ −2

Multiple Choice

Which point below is NOT part of the solution set?

• (0, -2)

• (1, 1)

• (3, 3)

• (2, 10)

Multiple Choice

Is (-2, 4) a solution to $$y<-2x-2$$  ?

• Yes

• No

Multiple Choice

Is (1, 6) a solution to the inequality $$y\ge-2x+1$$  ?

• Yes
• No

Multiple Choice

Which of the following inequalities matches the graph?

• y < -4x - 1
• y > -4x - 1
• y ≤ -4x - 1
• y ≥ -4x - 1

Multiple Choice

Which of the following inequalities matches the graph?

• y > 2x - 2
• y < 2x - 2
• y ≥ 2x - 2
• y ≤ 2x - 2

Multiple Choice

Which of the following inequalities matches the graph?

• x > -2

• x < -2

• y > -2

• y < -2

Multiple Choice

Which of the following inequalities matches the graph?

• x ≤ -4

• x ≥ -4

• y ≤ -4

• y ≥ -4

Multiple Choice

84 - 4x ≤ 52

• x > 8

• x < 8

• x > 8

• x < 8

Multiple Choice

Which graph represents x > 2

Multiple Choice

Solve $$\frac{x-6}{4}\le2$$  

• x ≤ 14

• x < 14

• x ≥ 14

• x = 14