Worksheet: Solve Inequalities using Addition & Subtraction | Pre ... - Free Printable

Let’s solve each inequality step by step. We’ll find the value of the variable that makes the inequality true, then graph it on a number line and write the solution in interval notation or as an inequality.

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1) y + 4 ≤ 5

Subtract 4 from both sides:
y ≤ 5 - 4
y ≤ 1

✔ Solution: y ≤ 1
Graph: A closed circle at 1 (because ≤ includes 1), and shade to the left.
Interval: (-∞, 1]

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2) x - 6 < -8

Add 6 to both sides:
x < -8 + 6
x < -2

✔ Solution: x < -2
Graph: An open circle at -2 (because < does NOT include -2), and shade to the left.
Interval: (-∞, -2)

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3) p + 3 > -2

Subtract 3 from both sides:
p > -2 - 3
p > -5

✔ Solution: p > -5
Graph: Open circle at -5, shade to the right.
Interval: (-5, ∞)

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4) q - 7 > -1

Add 7 to both sides:
q > -1 + 7
q > 6

✔ Solution: q > 6
Graph: Open circle at 6, shade to the right.
Interval: (6, ∞)

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5) 7 + d < 0

Subtract 7 from both sides:
d < 0 - 7
d < -7

✔ Solution: d < -7
Graph: Open circle at -7, shade to the left.
Interval: (-∞, -7)

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6) -8 + m ≤ -15

Add 8 to both sides:
m ≤ -15 + 8
m ≤ -7

✔ Solution: m ≤ -7
Graph: Closed circle at -7, shade to the left.
Interval: (-∞, -7]

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Final Answer:

1) y ≤ 1 → Graph: ●← at 1
2) x < -2 → Graph: ○← at -2
3) p > -5 → Graph: ○→ at -5
4) q > 6 → Graph: ○→ at 6
5) d < -7 → Graph: ○← at -7
6) m ≤ -7 → Graph: ●← at -7