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# help

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

Dec 2, 2019

#1
+109468
+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
0

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