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Solve each compound inequality (show your work!)


- 6 < 2x - 4 < 12


4x \leqslant 12 \: and - 7x \leqslant 21


15x > 30 \: or \: 18x < - 36

User Ombiro
by
4.9k points

1 Answer

5 votes

Answer: -1 < x < 8

x = 3

x ≠ 2

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

User Moritz Mahringer
by
5.3k points