Answer: -1 < x < 8
x = 3
x ≠ 2
Step-by-step explanation:
Isolate x in the middle. Perform operations to all 3 sides.
-6 < 2x - 4 < 12
+4 +4 +4
-2 < 2x < 16
÷2 ÷2 ÷2
-1 < x < 8
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Isolate x. Solve each inequality separately. Remember to flip the sign when dividing by a negative.
4x ≤ 12 and -7x ≤ 21
÷4 ÷4 ÷-7 ÷-7
x ≤ 3 and x ≥ 3
Since it is an "and" statement, x is the intersection of both inequalities.
When is x ≤ 3 and ≥ 3? when x = 3
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Isolate x. Solve each inequality separately.
15x > 30 or 18x < -36
÷15 ÷15 ÷18 ÷18
x > 2 or x < 2
Since it is an "or" statement, x is the union of both inequalities.
When we combine the inequalities, x is every value except 2.
x ≠ 2
