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

Options C, D, and E

Step-by-step 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

=

= -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.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions