Question

Solve the compound inequality.3x + 12 ≥ –9 and 9x – 3 ≤ 33 x ≥ –7 and x ≤ –4x ≥ 7 and x ≤ 4x ≥ 1 and x ≤ 4x ≥ –7 and x ≤ 4

Answer 1

To solve this problem, we will solve each inequality for x and the solution to the system will be the intersection of the solution sets.

1) Solving the first inequality for x we get:

`\begin{gathered} 3x+12\ge-9, \\ 3x\ge-9-12, \\ 3x\ge-21, \\ x\ge-(21)/(3), \\ x\ge-7. \end{gathered}`

2) Solving the second inequality for x we get:

`\begin{gathered} 9x-3\le33, \\ 9x\le33+3, \\ 9x\le36, \\ x\le(36)/(9), \\ x\le4. \end{gathered}`

Answer:

`x\ge-7\text{ and x }\le4.`