Question

Which values are in the solution set of the compound inequality –8 < 3x + 7 ≤ 10? Check all that apply.

–15
–5
–3
0
1
3

Answer 1

you can avoid algebra & simply calculate the expression's value with each of the answers

Answer 2

Options C, D, and E

Explanation:

To get the answer of this question we will simplify the inequality first.

-8 < 3x + 7 ≤ 10

We subtract (-7) in the given inequality

= -8 - 7 < (3x + 7) - 7 ≤ 10 - 7

= -15 < 3x ≤ 3

Now we will divide the inequality by 3

=
`-(15)/(3)<(3x)/(3)\leq (3)/(3)`

= -5 < x ≤ 1

Now the options which lie between (-5) to 1 and equal to 1 will be the solution set.

So the options will be (-3), 0 and 1

Options C, D, E will be the solutions.