Question

Solve the equation:

1. |x-7|=8
2. |x-9|=-14

Answer 1

1. x=-1 or x=15
2. no sol

Answer 2

1.
`x=-1; x=15`
2. Impossible

Explanation:

About #1.

There are two ways of reasoning.

Algebrically, you split the absolute value in two based on the sign of the quantity
`x-7`

`x-7 = 8; x\ge7\\x=15\\x-7=-8; x < 7\\x=-1`

Geometrically, and it's a personal preference of mine, you're asking to find the numbers that are 8 units away from 7. One is to the right (15), and the other is to the left (-1).

#2 is impossible. The modulus of a number is by definition non negative, so it can never be equal to a negative number.