Inequality With Visuals

Inequality With Visuals

Just the Big Ideas

Big Idea

Solutions to Inequalities are In the Shaded Regions

This works in both number lines and x-y graphs

Multiple Choice

Warmup: Solve this inequality on your whiteboard:

6x + 4 ≥ 8x - 18

• x ≤ 11

• x ≥ 2

• x ≤ -8

• x ≥ 6

Open circle means the number there isn't a solution. 11 is a solution to the top line, but not to the bottom line.

Open Ended

Write one solution to the inequality in this picture.

This is what Desmos shows you if you type in an inequality to solve.

​Dotted Line = Open Dot Uses < or >

​Solid Line = Closed Dot
Uses ≤ or ≥

Multiple Choice

8 - 5x < 10x + 23

What's the solution? [Use Desmos]

• x < 5

• x < 1

• x > -1

• x > 4

Multiple Select

Which of these are solutions to the inequality below? [Select more than one]

x + 3 > 2(-2x+4)

• -1

• 2/3

• 1

• 3

• 18

The >= greater or equal sign changes the line to solid, and then points on the line ARE solutions!

Need to Remember?

DOTTED = DON'T
SOLID = Sure

Multiple Select

Select all solutions to this inequality.

• (-1, 1)

• (0, 4)

• (4, 0)

• (-4, 4)

• (3, 1)

Open Ended

Explain why (-2, -2) is a solution to this inequality.

2 Inequalities: Solutions are in the twice-shaded zone (still not on dotted lines)

Multiple Choice

Which of these is NOT a solution to this system of inequalities?

• (4, -4)

• (8, 0)

• (6, 0)

• (4, -2)

Multiple Choice

Graph this system of inequalities. Is (-3, 2) a solution?

y > x + 4

-3x - y > 3

• YEAH

• NAH