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chrisitianmr66

11 december 2020 01:24

I'm tutoring a boy in your Algebra 1: Solving Equations and Inequalities, the section Compound Inequalties.

One of the quiz problems was to solve:

-8x>=24, to which the answer was x<=-3. The AND part was -13x>=52, to which the answer was x<=-4.

You said the answer was x<=-4.

However, if you put x=-3 into the right equation, you'd get 39>=52, which is incorrect.

If you put x=-4 into the left equation, you get 32>=24, which is true.

So x<= -3 must be the correct answer. That answer is also obvious looking at it on a numberline, since if you go left from -3, you also include the -4, but not vice versa.

What say you?

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Evan Lewis

12 december 2020 19:37
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Hi chrisitianmr66,

I took a look at this exercise and the answer that is marked as correct is x <= -4, which I believe is correct for this problem.

The solution for -8x>=24 is x<= -3 and the solution for -13x>=52 is x <= -4, like you said above. The solution to the compound inequality x <= -3 AND x <= -4 is x <= -4, since that is the more restrictive of the two solutions.

Here's a visual representation of the solution:

Since this is an AND inequality, the solution is the region where the two inequalities overlap, which would be x <= -4. A value of -3.5, for example, would only satisfy one of the inequalities, and all values in the solution range need to satisfy both inequalities since it is a compound AND inequality, which is why x <= -3 is an incorrect solution.

I hope this helps! Please let me know if you have any additional questions!

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