Practice worksheet for graphing linear inequalities on coordinate planes.

I'll solve this worksheet on graphing linear inequalities. Let me go through each problem step by step.

Problem 1: -4x < 8

Step 1: Solve for x
-4x < 8
Divide both sides by -4 (remember to flip the inequality sign when dividing by a negative):
x > -2

Step 2: Graph the solution
- Draw a vertical dashed line at x = -2 (dashed because it's a strict inequality, not "or equal to")
- Shade to the right of the line (since x > -2)

Problem 2: -2y ≤ -12

Step 1: Solve for y
-2y ≤ -12
Divide both sides by -2 (flip the inequality sign):
y ≥ 6

Step 2: Graph the solution
- Draw a horizontal solid line at y = 6 (solid because it's "or equal to")
- Shade above the line (since y ≥ 6)

Problem 3: -5x ≥ -40

Step 1: Solve for x
-5x ≥ -40
Divide both sides by -5 (flip the inequality sign):
x ≤ 8

Step 2: Graph the solution
- Draw a vertical solid line at x = 8 (solid because it's "or equal to")
- Shade to the left of the line (since x ≤ 8)

Problem 4: -6y ≥ 12

Step 1: Solve for y
-6y ≥ 12
Divide both sides by -6 (flip the inequality sign):
y ≤ -2

Step 2: Graph the solution
- Draw a horizontal solid line at y = -2 (solid because it's "or equal to")
- Shade below the line (since y ≤ -2)

Problem 5: -7x ≥ 28

Step 1: Solve for x
-7x ≥ 28
Divide both sides by -7 (flip the inequality sign):
x ≤ -4

Step 2: Graph the solution
- Draw a vertical solid line at x = -4 (solid because it's "or equal to")
- Shade to the left of the line (since x ≤ -4)

Problem 6: -3y ≥ 21

Step 1: Solve for y
-3y ≥ 21
Divide both sides by -3 (flip the inequality sign):
y ≤ -7

Step 2: Graph the solution
- Draw a horizontal solid line at y = -7 (solid because it's "or equal to")
- Shade below the line (since y ≤ -7)

This completes all six problems on the worksheet. Each involves solving a simple linear inequality and then graphing the solution on a coordinate plane.