Get Your Students Graphing Inequalities with These Top Worksheets ... - Free Printable

Let’s solve each inequality one by one. We’ll graph them on the coordinate plane as shown in your worksheet.

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7) x < -5

This means all points where the x-coordinate is less than -5.
→ Draw a dashed vertical line at x = -5 (dashed because it’s “less than”, not “less than or equal to”).
→ Shade everything to the left of that line.

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8) y ≤ (4/5)x - 4

First, graph the line y = (4/5)x - 4.
- When x = 0, y = -4 → point (0, -4)
- When x = 5, y = (4/5)(5) - 4 = 4 - 4 = 0 → point (5, 0)
Draw a solid line through these points (solid because of “≤”).
Now test a point NOT on the line — say (0,0):
Is 0 ≤ (4/5)(0) - 4? → 0 ≤ -4? No. So shade the side that does NOT include (0,0). That’s below the line.

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9) 3x - 2y < 10

Solve for y to make graphing easier:
3x - 2y < 10
→ -2y < -3x + 10
→ Divide by -2 (remember to flip the inequality sign!)
→ y > (3/2)x - 5

Graph the line y = (3/2)x - 5 with a dashed line (because of “>”).
Test (0,0): Is 0 > (3/2)(0) - 5? → 0 > -5? Yes! So shade the side that includes (0,0) — above the line.

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10) 5x - 3y ≤ -15

Solve for y:
5x - 3y ≤ -15
→ -3y ≤ -5x -15
→ Divide by -3 (flip inequality!)
→ y ≥ (5/3)x + 5

Graph line y = (5/3)x + 5 with a solid line.
Test (0,0): Is 0 ≥ (5/3)(0) + 5? → 0 ≥ 5? No. So shade the side that does NOT include (0,0) — above the line.

Wait — let me double-check that algebra:

Original: 5x - 3y ≤ -15
Subtract 5x: -3y ≤ -5x -15
Divide by -3 → y ≥ (5/3)x + 5 ✔ Correct.

But when we plug in (0,0), we get 0 ≥ 5? False → so shade opposite side → which is ABOVE the line? Wait — if the line has positive slope and y-intercept 5, then (0,0) is BELOW the line. Since (0,0) doesn’t satisfy, we shade ABOVE — yes, correct.

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11) y ≥ 4

Horizontal line at y = 4. Solid line (because of “≥”).
Shade everything above the line.

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12) x - y > 2

Solve for y:
x - y > 2
→ -y > -x + 2
→ Multiply by -1 (flip inequality!)
→ y < x - 2

Graph line y = x - 2 with dashed line.
Test (0,0): Is 0 < 0 - 2? → 0 < -2? No. So shade the side that does NOT include (0,0) — below the line.

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✔ All solved!

Final Answer:
You should have graphed each inequality as follows:

7) Dashed vertical line at x = -5, shaded left.
8) Solid line through (0,-4) and (5,0), shaded below.
9) Dashed line y = (3/2)x - 5, shaded above.
10) Solid line y = (5/3)x + 5, shaded above.
11) Solid horizontal line at y = 4, shaded above.
12) Dashed line y = x - 2, shaded below.