Solved Examples on Solving Inequalities with Multiplication and Division

Example 1: Solve: (x / 3) < 10

Solution:

(x/3) < 10

Multiply by 3 (3 is positive number so inequality does not flip)

3 × (x/3) < 10 × 3

⇒ x < 30

Example 2: Solve [y /(-4)] > 12

Solution:

[y /(-4)] > 12

Multiply by (-4) [-4 is negative number so inequality is flipped]

[y /(-4)] × (-4) < 12 × (-4)

⇒ y < -48

Example 3: Evaluate (z / 5) > 23

Solution:

(z / 5) > 23

Multiply by 5 (5 is positive number so inequality does not flip)

(z / 5) × 5 > 23 × 5

⇒ z > 115

Example 4: Solve (p/ (-6)) < 2

Solution:

(p/ (-6)) < 2

Multiply by (-6) [-6 is negative number so inequality is flipped]

(p/ (-6)) × (-6) > 2 × (-6)

⇒ p > -12

Example 5: Solve x / 3 ≤ -15

Solution:

x / 3 ≤ -15

Multiply by 3

x ≤ -15 × 3

⇒ x ≤ -45

Example 6: Solve (-3x) ≤ -15

Solution:

(-3x) ≤ -15

Divide by -3

(-3x) / (-3) ≥ -15 / (-3)

⇒ x ≥ 5

Example 7: Solve 8x > 16

Solution:

8x > 16

Divide by 8

x > 16 / 8

⇒ x > 2

Example 8: Solve -12y < 36

Solution:

-12y < 36

Divide by -12

y > 36 / (-12)

⇒ y > -3

In this article we will explore how to solve Inequalities with Multiplication and Division in detail and solve some examples related to it. Let’s start our learning on the topic “Solving Inequalities with Multiplication and Division.”