How do you solve for x: 2|x − 3| + 4 = 62|x−3|+4=6?
1 Answer
Explanation:
"the expression inside the absolute value can be positive"the expression inside the absolute value can be positive
"or negative, hence there are 2 possible solutions"or negative, hence there are 2 possible solutions
"isolate "|x-3|isolate |x−3|
"subtract 4 from both sides"subtract 4 from both sides
rArr2|x-3|=2⇒2|x−3|=2
"divide both sides by 2"divide both sides by 2
rArr|x-3|=1⇒|x−3|=1
color(magenta)"Positive expression"Positive expression
x-3=1rArrx=1+3=4x−3=1⇒x=1+3=4
color(magenta)"Negative expression"Negative expression
-(x-3)=1−(x−3)=1
rArr-x+3=1⇒−x+3=1
rArr-x=1-3=-2rArrx=2⇒−x=1−3=−2⇒x=2
color(blue)"As a check"As a check Substitute these values into the left side and if equal to the right side then they are the solutions.
x=2to2|-1|+4=(2xx1)+4=6x=2→2|−1|+4=(2×1)+4=6
x=4to2|1|+4=(2xx1)+4=6x=4→2|1|+4=(2×1)+4=6
rArrx=2" or "x=4" are the solutions"⇒x=2 or x=4 are the solutions
