Question

Select all of the following inequalities with the solution: x^2

A) 3x - 2(x - 2) < 6
B) 8x + 5 < 9
C) -12(2x - 6) > 12
D) 3 > 2 + 1

Answer 1

To solve these inequalities, isolate the variable x on one side of the inequality sign. A) x < 2, B) x < 0.5, C) x < 2.5, D) No solution for x.

Step-by-step explanation:

To solve these inequalities, we need to isolate the variable x on one side of the inequality sign. Here are the steps to solve them:

A) 3x - 2(x - 2) < 6
First distribute -2, which gives us 3x - 2x + 4 < 6
Combine like terms, giving us x + 4 < 6
Then subtract 4 from both sides, resulting in x < 2.

B) 8x + 5 < 9
First subtract 5 from both sides, which gives us 8x < 4
Then divide both sides by 8, resulting in x < 0.5.

C) -12(2x - 6) > 12
First distribute -12, which gives us -24x + 72 > 12
Then subtract 72 from both sides, giving us -24x > -60
Finally, divide both sides by -24 (note: when dividing by a negative number, the inequality sign must be flipped), resulting in x < 2.5.

D) 3 > 2 + 1
Simplify the right side of the inequality, which gives us 3 > 3.
This inequality is false, so there is no solution for x.