# How do you solve the equation #2abs(5x+1)-3=0#?

##### 3 Answers

Given:

Add 3 to both sides:

Divide both sides by 2

Separate into two equations without the absolute value function, one with the right side positive and the other with the right side negative:

Subtract one from both sides of both equations:

Divide both sides of both equations by 5:

Check:

Both values check.

#### Explanation:

We know either

Let's solve the first one

Divide both sides by 5

Solve the second one

Divide both sides by 5

Therefore,

#### Explanation:

#"isolate the absolute value"#

#"add 3 to both sides"#

#2|5x+1|cancel(-3)cancel(+3)=0+3#

#rArr2|5x+1|=3#

#"divide both sides by 2"#

#cancel(2)/cancel(2)|5x+1|=3/2#

#rArr|5x+1|=3/2#

#"the expression inside the absolute value can be"#

#"positive or negative"#

#color(blue)"Solution 1"#

#5x+1=3/2#

#"subtract 1 from both sides"#

#rArr5x=1/2#

#"dividing both sides by 5 gives"#

#rArrcolor(red)(bar(ul(|color(white)(2/2)color(black)(x=1/10)color(white)(2/2)|)))#

#color(blue)"Solution 2"#

#-(5x+1)=3/2#

#rArr-5x-1=3/2#

#"add 1 to both sides"#

#rArr-5x=5/2#

#"divide both sides by - 5"#

#rArrcolor(red)(bar(ul(|color(white)(2/2)color(black)(x=-1/2)color(white)(2/2)|)))#