Answer:
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To find the compound inequality for the statement "3x ≤ 4x - 5 ≤ 39," you can break it down into two separate inequalities and then combine them into a compound inequality:
3x ≤ 4x - 5
4x - 5 ≤ 39
Now, solve each inequality separately:
3x ≤ 4x - 5
Subtract 4x from both sides to isolate x:
3x - 4x ≤ -5
-x ≤ -5
Now, multiply both sides by -1. Remember that when you multiply or divide by a negative number, you must reverse the inequality sign:
x ≥ 5
So, the solution to the first inequality is x ≥ 5.
4x - 5 ≤ 39
Add 5 to both sides to isolate 4x:
4x ≤ 39 + 5
4x ≤ 44
Now, divide both sides by 4:
x ≤ 44/4
x ≤ 11
So, the solution to the second inequality is x ≤ 11.
Now, combine these two inequalities into a compound inequality:
x ≥ 5 and x ≤ 11
You can represent this compound inequality as:
5 ≤ x ≤ 11
This is the compound inequality for the given statement "3x ≤ 4x - 5 ≤ 39."
Step-by-step explanation: Hope this helps