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Assignment 3.6: Absolute Value Functions
Score: $1.25 / 13$ Answered: $3 / 13$
Question 4
Solve $|x|=9$
$x=$ $\square$
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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: