Questions: Solve x=9 x=

Transcript text: Cosumnes River College | Cosumnes River College My Apps Assignment 3.6: Absolute Value Functions Score: $1.25 / 13$ Answered: $3 / 13$ Question 4 Solve $|x|=9$ $x=$ $\square$ To give multiple answers, list your answers separated by a comma Question Help: Video Submit Question

Solution

Solution Steps

To solve the equation $ |x| = 9 $, we need to find the values of $ x $ that satisfy this condition. The absolute value equation $ |x| = a $ has two solutions: $ x = a $ and $ x = -a $. Therefore, for $ |x| = 9 $, the solutions are $ x = 9 $ and $ x = -9 $.

Step 1: Understanding the Absolute Value Equation

The equation given is $ |x| = 9 $. The absolute value of a number $ x $ is the distance of $ x $ from zero on the number line, which means it is always non-negative. Therefore, the equation $ |x| = 9 $ implies that the distance of $ x $ from zero is 9.

Step 2: Solving the Absolute Value Equation

The equation $ |x| = a $ has two possible solutions: $ x = a $ and $ x = -a $. Applying this to our equation $ |x| = 9 $, we have: