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Solve and write interval notation for the solution set. show work

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1 Answer

This is done exactly as algebraic equations, but it is instead simply an inequality - x will be greater than, less than, etc., anything but equal.

6-2x<or=-2
1. -2x<or=-8 (subtract 6 from each side);
2. X<or=4

-1/5x>2
1. -5 * -1/5x>2*-5 (multiply both sides by -5);
2. X>-10

Interval notation starts with the lowest value & goes toward the highest value, with x in the middle:

-10<x<or=4

Notice that we had to turn x>-10 backward, in order to show that there are values of x in between -10 & 4 that are the solution set. As my iPhone doesn't seem to offer me a "greater than or equal to" sign, I have made a variation here that I believe is comprehensible. You will use the standard sign.

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