Identify the solution set for: −2|−2x−4|=−12 A: {5,1} B: {−5,1} C: {−5,−1} D: No Solution

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C: {−5, 1)

Step-by-step explanation:

Starting with −2|−2x−4|=−12, divide both sides by -2:

|−2x−4| =  6

Reduce this by dividing all terms by 2:

|-x - 2| = 3

This is equivalent to   x + 2 = 3  and  x + 2 = - 3

Solving thse two equations, we get x = 1 and x = -5

And so the solution set is  C: {−5, 1)

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step-by-step explanation:

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we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4