Question

How do you solve `|-7x + 7| = 14`?

Answer 1

`x=-1`
`x=3`

Explanation:

`-7x+7=14`
or
`-7x=14-7`
or
`-7x=7`
or
`x=-7/7`
or
`x=-1`................Ans`1`

Now consider
`-7x+7=-14`
or
`-7x=-14-7`
or
`-7x=-21`
or
`7x=21`
or
`x=21/7`
or
`x=3`.....................Ans`2`

Answer 2

`x= -1" and "x=3" "` are solutions

Explanation:

Remember that everything inside the two | | is read as positive. This is called an 'absolute' value

Written as in the question or as 'abs(-7x+7)=14'

`color(brown)("Observe where the red and blue lines cross. It is evident that this")` `color(brown)("expression gives two values for "x" as an answer.")`

The part of the equation inside the | | may be positive or negative but will always be read as a final positive overall value.

Thus what is inside the | | has the possibility to be -14 or +14 and still satisfy the equation

Suppose `-7x+7=14`

`color(blue)("Then "-7x=7" " =>" " x=(-1))`

Suppose `-7x+7=-14`

`color(blue)("Then "-7x=-21" "=>" "x=3)`