Question

How many solutions are there to the equation x^2 = 1? Explain how you know.

Answer 1

Two solutions

Explanation:

Let's clear the variable x.

Since x is squared we apply square root to clear

`x^2=1\\√(x^2)= 1`

We have the following term
`√(x^2)`

This term corresponds to the formula of a absolute value of a number.

The absolute value of a number is its distance from zero on a number line

`x^2=1\\√(x^2)= 1\\\|x\|=1`

`x=1\\x=-1`

the absolute value of x is equal to 1 this means that x takes all the values that are at a distance of one unit from zero on the real line

The numbers that have a distance of 1 unit from zero would be 1 and also -1 (as it is a distance the module is always positive)