Question

solve each of these inequalities and show your answer on a number line and using interval notation.[ Note: there are 3 inequalities.]4(x + 2) <- 6x + 8

Answer 1

EXPLANATION

Given the inequality:

4(x+2) < -6x +8

Applying distributive property:

4x + 8 ≤ 6x + 8

Adding -6x to both sides:

4x - 6x + 8 ≤ 6x -6x + 8

Adding similar terms:

-2x + 8 ≤ 8

Subtracting -8 to both sides:

-2x +8 -8 ≤ 8 - 8

Adding similar terms:

-2x ≤ 0

Multiply both sides by -1 (Reverse the inequality)

2x ≥ 0

Dividing both sides by 2:

x ≥ 0

The answer in interval notation is:

[0,∞)