Solve the absolute value equation
|x+1|=|2x-6|​

x = 5, and/or x= - 7/3

Step-by-step explanation:

|x+1|=|2x+6|

We know eitherx+1=2x+6orx+1=−(2x+6)

x+1=2x+6(Possibility 1)

x+1−2x=2x+6−2x(Subtract 2x from both sides)

−x+1=6

−x+1−1=6−1 (Subtract 1 from both sides)

−x=5

(Divide both sides by -1)

x=−5

x+1=−(2x+6)(Possibility 2)

x+1=−2x−6(Simplify both sides of the equation)

x+1+2x=−2x−6+2x(Add 2x to both sides)

3x+1=−6

3x+1−1=−6−1(Subtract 1 from both sides)

3x=−7

Divide both sides by 3

x= −7 / 3

Check answers. (Plug them in to make sure they work.)

x=−5(Works in original equation)

x= −7/3

(Works in original equation)

x=−5 or x= −7 / 3

360/29

step-by-step explanation: