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

Accepted Solution

Answer:Two solutions Step-by-step explanation:Let's clear the variable x.Since x is squared we apply square root to clear[tex]x^2=1\\\sqrt{x^2}= 1[/tex]We have the following term [tex]\sqrt{x^2}[/tex] 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[tex]x^2=1\\\sqrt{x^2}= 1\\\|x\|=1[/tex] [tex]x=1\\x=-1[/tex]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 lineThe 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)