Solving Linear Inequalities (A) worksheet featuring ten algebraic inequalities to solve.

Let’s solve each inequality one by one. We’ll isolate the variable on one side of the inequality sign, just like solving equations — but remember: if you multiply or divide by a negative number, flip the inequality sign! (We won’t need to do that here though.)

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1. 4 ≤ 4 + z

Subtract 4 from both sides:

4 - 4 ≤ 4 + z - 4
0 ≤ z
So, z ≥ 0

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2. g - 4 ≤ -8

Add 4 to both sides:

g - 4 + 4 ≤ -8 + 4
g ≤ -4

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3. 5 ≤ -b - 4

Add 4 to both sides:

5 + 4 ≤ -b - 4 + 4
9 ≤ -b

Now multiply both sides by -1 → FLIP the inequality:

-9 ≥ b
or b ≤ -9

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4. 7 ≥ -q + 9

Subtract 9 from both sides:

7 - 9 ≥ -q + 9 - 9
-2 ≥ -q

Multiply both sides by -1 → FLIP the inequality:

2 ≤ q
or q ≥ 2

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5. 6 - n ≤ -5

Subtract 6 from both sides:

6 - n - 6 ≤ -5 - 6
-n ≤ -11

Multiply both sides by -1 → FLIP the inequality:

n ≥ 11

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6. 1 > -a + 3

Subtract 3 from both sides:

1 - 3 > -a + 3 - 3
-2 > -a

Multiply both sides by -1 → FLIP the inequality:

2 < a
or a > 2

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7. -n + 3 > 6

Subtract 3 from both sides:

-n + 3 - 3 > 6 - 3
-n > 3

Multiply both sides by -1 → FLIP the inequality:

n < -3

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8. -8 - a ≥ -5

Add 8 to both sides:

-8 - a + 8 ≥ -5 + 8
-a ≥ 3

Multiply both sides by -1 → FLIP the inequality:

a ≤ -3

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9. 5 - r < -8

Subtract 5 from both sides:

5 - r - 5 < -8 - 5
-r < -13

Multiply both sides by -1 → FLIP the inequality:

r > 13

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10. 6 ≤ -w + 2

Subtract 2 from both sides:

6 - 2 ≤ -w + 2 - 2
4 ≤ -w

Multiply both sides by -1 → FLIP the inequality:

-4 ≥ w
or w ≤ -4

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Final Answer:
1. z ≥ 0
2. g ≤ -4
3. b ≤ -9
4. q ≥ 2
5. n ≥ 11
6. a > 2
7. n < -3
8. a ≤ -3
9. r > 13
10. w ≤ -4