Question

Solve the following inequality. 21 ≤ -3(x-4) < 30

Answer 1

C. -6 < x ≤ -3

Answer 2

`-6<x\leq -3`

Explanation:

The process of solving inequalities like this is similar to the process of solving equations. Isolate the variable x, and whatever you do to one side, do to the other sides.

1) First, distribute the -3 to the terms inside the parentheses:

`21\leq -3(x-4)<30\\21 \leq -3x+12< 30\\`

2) Next, subtract 12 from all three sides:

`21 \leq -3x+12< 30\\9\leq -3x<18`

3) Finally, divide all three sides by -3. However, remember that whenever you divide numbers on different sides by a negative number, you need to flip the signs to make them face the other way:

`9\leq -3x<18\\-3\geq x>-6`

Thus,
`-3\geq x>6` is the answer. Normally, answers are written with the numbers going from least to greatest, so you could also write it like this and it would still be correct, too:

`-6<x\leq -3`