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Solve |2x + 1| = |4x + 3|.

 Dec 2, 2019
 #1
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+1

The easiest way to do this is to square both sides but you have to check the answers that you get because some may be invalid.

 Dec 2, 2019
 #2
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Squaring both sides as melody said. we get: 

(2x+1)^2=(2x+1)(2x+1)=4x^2+2x+2x+1=4x^2+4x+1 

(4x+3)^2=(4x+3)(4x+3)=16x^2+12x+12x+9=16x^2+24x+9 

So we have

 

\(4x^2+4x+1=16x^2+24x+9\)

Subtract 1 

\(4x^2+4x=16x^2+24x+8\)

subtract 4x 

\(4x^2=16x^2+20x+8\)

Rearrange 

\(16x^2+20x+8=4x^2\)

Subtract 4x^2

\(12x^2+20x+8=0\)

Factor 4

\(4(3x^2+5x+2)\)=0

\(3x^2+5x+2=0\)

x=\(\frac{-2}{3}\) or -1 

Subsituite back and check 

2(-1)+1=4(-1)+3 

-1 = -1 correct! 

-1 is a solution 

Subsituite -2/3 and check, Correct! 

 Dec 2, 2019

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