SOLVING INEQUALITIES BY MULTIPLYING OR DIVIDING

Use a table to solve the inequality.

Problem 1 :

4x < 4

Solution :

4x < 4

Divide it by 4 both sides.

4x/4 < 4/4

x < 1

Problem 2 :

-2x ≤ 2

Solution :

-2x ≤ 2

Divide by -2 on both sides.

x ≥ 2/(-2)

x ≥ -1

Problem 3 :

-5x > 15

Solution :

-5x > 15

Divide it by -5 on both sides.

x < 15/(-5)

x < -3

Problem 4 :

x/-3 ≥ 1

Solution :

x/-3 ≥ 1

Divide it by -3 on both sides.

x ≤ 1/(-3)

x ≤ -3

Problem 5 :

x/-2 > 5/2

Solution :

x/-2 > 5/2

Multiply by -2 on both sides.

x < -5

Problem 6 :

x/4 ≤ 3/8

Solution :

x/4 ≤ 3/8

Multiply by 4 on both sides, we get

x ≤ (3/8)⋅4

x ≤ (3/2)

Solve the inequality. Graph the solution.

Problem 1 :

3n > 18

Solution :

3n > 18

Divide each side by 3.

3n/3 > 18/3

n > 6

Problem 2 :

c/4 ≤ -9

Solution :

c/4 ≤ -9

Multiply each side by 4.

(c/4) × 4 ≤ -9 × 4

c ≤ -36

Problem 3 :

1.2m < 12

Solution :

1.2m < 12

Divide each side by 1.2.

(1.2/1.2)m < 12/1.2

m < 10

Problem 4 :

-14 > x ÷ 2

Solution :

-14 > x ÷ 2

Multiply each side by 2.

-14 × 2 > (x/2) × 2

-28 > x

Problem 5 :

w/5 ≥ -2.6

Solution :

w/5 ≥ -2.6

Multiply each side by 5.

(w/5) × 5 ≥ -2.6 × 5

w ≥ -13

Problem 6 :

5 < 2.5k

Solution :

Given, 5 < 2.5k

Divide each side by 2.5.

5/2.5 < 2.5/2.5k

2 < k

k > 2

Problem 7 :

4x ≤ -3/2

Solution :

Given, 4x ≤ -3/2

Multiply each side by 2.

(4x) × 2 ≤ (-3/2) × 2

8x ≤ -3

Divide each side by 8.

(8x)/8 ≤ -3/8

x ≤ -3/8

Problem 8 :

2.6y ≤ -10.4

Solution :

Given, 2.6y ≤ -10.4

Divide each side by 2.6.

2.6/2.6y ≤ -10.4/2.6

y ≤ -4

Problem 9 :

10.2 > b/3.4

Solution :

Given,10.2 > b/3.4

Multiply each side by 3.4.

10.2 × 3.4 > (b/3.4) × 3.4

34.68 > b

b < 34.68