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Find the compound inequality for 3x less than or equal to 4x-5 les than or equal to 39

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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

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