**Solving inequalities with addition and subtraction worksheet :**

Worksheet on solving inequalities with addition and subtraction is much useful to the students who would like to practice problems on inequalities.

1. Solve the inequality given below. Graph and check the solution.

x + 5 < -12

2. Solve the inequality given below. Graph and check the solution.

8 ≤ y - 3

3. Solve the inequality given below. Graph and check the solution.

x + 3 < 8

4. Solve the inequality given below. Graph and check the solution.

y -5 ≥ -7

5. Solve the inequality given below. Graph and check the solution.

21 > 12 + x

**Problem 1 : **

Solve the inequality given below. Graph and check the solution.

x + 5 < -12

**Solution :**

**Step 1 : **

Solve the inequality

x + 5 < -12

Use the Subtraction Property of Inequality.

Subtract 5 on from both sides.

(x + 5) - 5 < -12 - 5

x < -17

**Step 2 : **

Graph the solution.

**Step 3 :**

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute -18 for x into x + 5 < -12.

-18 + 5 < -12

-13 < -12

The inequality is true.

**Problem 2 : **

Solve the inequality given below. Graph and check the solution.

8 ≤ y - 3

**Solution :**

**Step 1 : **

Solve the inequality

8 ≤ y - 3

Use the Addition Property of Inequality.

Add 3 to to both sides.

8 + 3 ≤ (y - 3) + 3

11 ≤ y

or y ≥ 11

**Step 2 : **

Graph the solution.

**Step 3 :**

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute 12 for y into 8 ≤ y - 3.

8 ≤ 12 - 3

8 ≤ 9

The inequality is true.

**Problem 3 : **

Solve the inequality given below. Graph and check the solution.

x + 3 < 8

**Solution :**

**Step 1 : **

Solve the inequality

x + 3 < 8

Use the Subtraction Property of Inequality.

Subtract 3 from both sides.

(x + 3) - 3 < 8 - 3

x < 5

**Step 2 : **

Graph the solution.

**Step 3 :**

Check the solution. Substitute a solution from the shaded part of your number line into the original inequality.

Substitute 0 for x into x + 3 < 8.

0 + 3 < 8

3 < 8

The inequality is true.

**Problem 4 : **

Solve the inequality given below. Graph and check the solution.

y -5 ≥ -7

**Solution :**

**Step 1 : **

Solve the inequality

y -5 ≥ -7

Use the Addition property Property of Inequality.

Add 5 to both sides.

(y -5) + 5 ≥ -7 + 5

y ≥ -2

**Step 2 : **

Graph the solution.

**Step 3 :**

Substitute 1 for y into y -5 ≥ -7.

1 - 5 ≥ -7

-4 ≥ -7

The inequality is true.

**Problem 5 : **

Solve the inequality given below. Graph and check the solution.

21 > 12 + x

**Solution :**

**Step 1 : **

Solve the inequality

21 > 12 + x

Use the Subtraction property Property of Inequality.

Subtract 12 from both sides.

21 - 12 > (12 + x) - 12

9 > x

or x < 9

**Step 2 : **

Graph the solution.

**Step 3 :**

Substitute 2 for x into 21 > 12 + x.

21 > 12 + 2

21 > 14

The inequality is true.

After having gone through the stuff given above, we hope that the students would have understood "Solving inequalities with addition and subtraction worksheet".

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