Question

Which graph represents the solution set of the compound inequality -4≤3x-1 and 2x+4≤18?

Answer 1

I solved for x in each case and got
x
`\geq`-1 and x
`\leq`7

So the first graph would apply

Answer 2

we have

`-4\leq 3x-1` ----> inequality A

`-4\leq 3x-1 \\-4+1 \leq 3x\\-3 \leq 3x\\-1\leq x\\ x\geq-1`

The solution of the inequality A is the interval ------> [-1,∞)

`2x+4\leq 18` -------> inequality B

`2x \leq 18-4`

`x \leq 14/2`

`x \leq 7`

The solution of the inequality B is the interval ------> (-∞,7]

The solution of the compound inequality is

[-1,∞) ∩ (-∞,7]=[-1,7]

therefore

the answer in the attached figure