Question

13. Solve the following inequalities: a. 3x - 3 > 6 b. 24x + 4 < 52 c. -2x - 2 < 8 d. 10x - 100 > 0

Answer 1

a. 3x - 3 > 6

3x>6+3

3x>9

x>9/3=3

x∈[3, +∞[

b. 24x + 4 < 52

24x<52-4

24x<48

x<2

x∈]-∞, 2]

c. -2x - 2 < 8

2-x<8+2

-2x<10

-x<102=-5

x>5

x[5, +∞[

d. 10x - 100 > 0

10x>100

x>10

x∈[10, +∞[

Explanation:

Answer 2

View below

Explanation:

In order to solve these inequalities, we need to isolate x.

#1. 3x - 3 > 6

3x > 6 + 3 {add 3 to both sides}

3x > 9 {simplify}
x > 3

#2. 24x + 4 < 52

24x < 52 - 4 {subtract 4 from both sides}

24x < 48 {divide both sides by 24}

x < 2

#3. -2x - 2 < 8

-2x < 8 + 2 {add 2 to both sides}

-2x < 10 {divide both sides by -2}

x > -5

#4. 10x - 100 > 0

10x > 100 + 0 {add 100 to both sides}

10x > 100 {divide both sides by 10}

x > 10

Therefore, these are the solutions to our inequalities.