Question

What is 9| - z/3| + 6 < 30

Answer 1

`9|- (z)/(3) | + 6 \ \textless \ 30 \\ \\ 9 * (z)/(3) + 6 \ \textless \ 30 \\ \\ 3z + 6 \ \textless \ 30 \\ \\ 3z \ \textless \ 30 - 6 \\ \\ 3z \ \textless \ 24 \\ \\ z \ \textless \ (24)/(3) \\ \\ z \ \textless \ 8 \\ \\ Answer: z \ \textless \ 8`

Answer 2

9|⁻¹/₃z| + 6 < 30
9|⁻¹/₃z| + 6 < ±30
9|⁻¹/₃z| + 6 < 30 or 9|⁻¹/₃z| + 6 > -30
9(¹/₃z) + 6 < 30 or 9(¹/₃z) + 6 > -30
3z + 6 < 30 or 3z + 6 > -30
- 6 - 6 - 6 - 6
3z < 24 or 3z > -24
3 3 3 3
z < 8 or z > -8

Solution Set: z and (-∞, 8) or (-8, ∞)