# How do you solve the equation #abs(4/3-2/3x)=3/4#?

##### 2 Answers

*and*

#### Explanation:

Absolute value equations are a little tough. Some teachers say that they "make numbers positive", but that doesn't mean *distance*. That's why they "make the number positive"; because there's no such thing as a negative distance (we can't have

When we have

So, the way we solve for absolute value equations is to let one equation be positive and another be negative:

**Positive situation**

*subtract #4/3# on both sides*

*divide by #-2/3#*

**Negative solution**

*divide by #-1# on both sides*

*subtract #4/3# on both sides*

*divide by #-2/3# on both sides*

So, our solutions are *and*

graph{y=abs(4/3-2/3x)-3/4}

Yep, intercepts at

#### Explanation:

#"However, the value of the expression inside the bars"#

#"can be positive or negative"#

#"This means there are 2 possible solutions to the equation"#

#color(red)(+-)(4/3-2/3x)=3/4#

#color(blue)"First possible solution"#

#4/3-(2x)/3=3/4larrcolor(red)" positive value"#

#rArr(2x)/3=4/3-3/4=7/12#

#rArr24x=21larrcolor(red)" cross-multiplying"#

#rArrx=21/24=7/8larrcolor(magenta)" first possible solution"#

#color(blue)"Second possible solution"#

#(2x)/3-4/3=3/4larrcolor(red)" negative value"#

#rArr(2x)/3=3/4+4/3=25/12#

#rArr24x=75larrcolor(red)" cross-multiplying"#

#rArrx=75/24=25/8larrcolor(magenta)" second possible solution"#

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

#|4/3-(2/3xx7/8)|=|4/3-7/12|=|3/4|=3/4#

#|4/3-(2/3xx25/8)|=|4/3-25/12|=|-3/4|=3/4#

#rArrx=7/8" or " x=25/8" are the solutions"#