Question

What is the solution set for the following inequality? 2x + 8x ≥ 15 + 14x + 9

Answer 1

move all x variables to one side so
10x ≥ 14x + 24
-4x ≥ 24
divide both sides by negative therefore sign switches therefore final answer
x ≤ -6

Answer 2

x ≤ -6

Explanation:

Given the inequality statement: 2x + 8x ≥ 15 + 14x + 9

Add like terms:

2x + 8x ≥ 15 + 14x + 9

10x ≥ 24 + 14x

Subtract 14x from both sides:

10x - 14x ≥ 24 + 14x - 14x

-4x ≥ 24

Divide both sides by -4, while flipping the inequality symbol (according to the division property of inequality, the symbol flips when you multiply or divide both sides by a negative number):

`(-4x)/(-4) \leq (24)/(-4)`

x ≤ -6

Therefore, the solution is: x ≤ -6, interval notation: (- ∞, -6].