Solve -4 < -2x + 6 < 14.
Hint
Look out for sign shenanigans.
Answer
-4 < x < 5
Solve 2x < 3x + 2 or 4x ≥ 5x – 3
Check your solutions against a number line: they cover more than you might think.
The inequalities come out to x > -2 or x ≤ 3. Between the two, that covers all the real numbers, so our solution is "all real numbers."
Solve -12 ≤ 4x ≤ 10.
A little division never hurt anyone, especially when it's so positive.
Solve -5x > x + 18 or 2x – 4 ≤ 3x – 4.
The first inequality simplifies to x < -3.
x < -3 or x ≥ 0
5 < -3x + 7 < 11
Flip every sign around when dividing by a negative.
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