Answer:
[tex] \sf \large \: x=7 or x=−3[/tex]
Step-by-step explanation:
Let's solve your equation step-by-step.
|x+8|=|2x+1|
Solve Absolute Value.
|x+8|=|2x+1|
We know eitherx+8=2x+1orx+8=−(2x+1)
x+8=2x+1(Possibility 1)
x+8−2x=2x+1−2x(Subtract 2x from both sides)
−x+8=1
−x+8−8=1−8(Subtract 8 from both sides)
−x=−7
−x/−1 = −7/−1
(Divide both sides by -1)
x=7
x+8=−(2x+1)(Possibility 2)
x+8=−2x−1(Simplify both sides of the equation)
x+8+2x=−2x−1+2x(Add 2x to both sides)
3x+8=−1
3x+8−8=−1−8(Subtract 8 from both sides)
3x=−9
3x/3 = −9/3
(Divide both sides by 3)
x=−3
Check answers. (Plug them in to make sure they work.)
x=7(Works in original equation)
x=−3(Works in original equation)
