ShmoopTube

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Here's another shmoop du jour...

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Graph the inequality -4 ≤ -2x < 6.

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And here are your potential answers...

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As with all of these kinds of problems, there

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are really two inequalities here...the first is: negative 4 is less than or equal to negative 2x.

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To isolate x we need to divide both sides by negative 2...

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To isolate x we need to divide both sides by negative 2 and… a red light should be

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Whenever we divide or multiply an inequality by a negative, we have to flip the sideways

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ice cream cone once

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around...x is less than or equal to 2.

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Well, we have a starting point.

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On our number line we mark the 2... and since it's less than OR equal to, it means that

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the dot has to be filled in...

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So B and C don't work... and neither does A, which starts at 3 rather than 2.

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We know that x is LESS than 2, meaning that it's gonna live somewhere

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over here...

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The only one left that might work is D... but just to be sure let's check out the 2nd

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part of the equation.

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We have negative 2x is less than 6... Divide both sides by negative 2, flip around

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the sideways ice cream cone thingy...

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...and we have x is greater than negative 3.

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So yep, the answer is indeed D.

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