Solve the inequality

Question

A. 2(3-x)≥14

B. -3x-3(x+1)<9

C. 3(2x-4)+1>2(2x-3)-8

Answer 1

Don't forget that solving algebraic inequalities works the same as solving algebraic equations, with one exception: when you divide or multiply both sides of an inequality by a negative number, you must "flip" the inequality symbol. Everything else is the same, including PEMDAS. All three of these problems have parentheses, so I will get rid of those first using the distributive method. I will then isolate the variable and combine like terms to solve.

A.

2(3 - x) ≥ 14

6 - 2x ≥ 14

-2x ≥ 8

x ≤ -4 (flipped, because we divided by -2)

B.

-3x - 3(x + 1) < 9

-3x - (3x + 3) < 9

-3x - 3x - 3 < 9

-6x - 3 < 9

-6x < 12

x > -2 (flipped, because we divided by -6)

C.

3(2x - 4) + 1 > 2(2x - 3) - 8

6x - 12 + 1 > 4x - 6 - 8

6x - 11 > 4x - 14

2x - 11 > -14

2x > -3

x > -3/2 (we do not flip because we are dividing by positive 2)