Answer:
-4 < x ≤ -3
Step-by-step explanation:
The compound inequality needs to be separated into its two parts in order to obtain a solution.
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We can do a little preliminary work to make the solutions easier.
2x +6 ≤ x +3 < 3x +11 . . . . . given
x +3 ≤ 0 < 2x +8 . . . . . . . . subtract x+3
<h3>left side</h3>x +3 ≤ 0
x ≤ -3 . . . . . . . subtract 3
<h3>right side</h3>0 < 2x +8
0 < x +4 . . . . divide by 2
-4 < x . . . . . . subtract 4
<h3>solution</h3>Now, we can rearrange these back into a compound inequality.
-4 < x ≤ -3
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The graphing calculator shows the same solution.
