# How do you solve #|2x+5| = 3x+4# and find any extraneous solutions?

##### 2 Answers

#### Answer:

Non-extraneous solution

#### Explanation:

Given

One method of solving this would be to square both sides:

Simplifying

Factoring

Giving potential solutions

Checking these against the original equation:

Since

this solution is extraneous.

#### Answer:

#### Explanation:

This equation has 2 solutions.

#rArr2x+5=color(red)(+-)3x+4#

#• " solve " 2x+5=3x+4# subtract 2x from both sides.

#cancel(2x)cancel(-2x)+5=3x-2x+4#

#rArr5=x+4# subtract 4 from both sides.

#5-4=xcancel(+4)cancel(-4)#

#rArrx=1larrcolor(red)" to be verified"#

#• " solve " 2x+5=color(red)(-)(3x+4)#

#rArr2x+5=-3x-4# add 3x to both sides.

#2x+3x+5=cancel(-3x)cancel(+3x)-4#

#rArr5x+5=-4# subtract 5 from both sides.

#5xcancel(+5)cancel(-5)=-4-5#

#rArr5x=-9# divide both sides by 5

#(cancel(5) x)/cancel(5)=(-9)/5#

#rArrx=-9/5larrcolor(red)" to be verified"#

#color(blue)"As a check"# Substitute these values into the equation and if the left side equals the right side then they are the solutions.

#x=1to|2+5|=3+4to7=7to" true"#

#x=-9/5to|-18/5+25/5|=-27/5+20/5to7/5=-7/5to" false"#

#rArrx=1" is the solution"#

#rArrx=-9/5" is an extraneous solution"#