Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 09, 2024

Find the solutions for the absolute value equation $|x| = 9$ .

STEP 1

Assumptions
1. We need to find the value of $x$ such that the absolute value of $x$ is equal to 9.
2. The absolute value function, denoted $|x|$ , returns the non-negative value of $x$ .

STEP 2

The definition of absolute value states that if $|x| = a$ , then $x = a$ or $x = -a$ for any positive number $a$ .

STEP 3

Since $|x| = 9$ , we apply the definition of absolute value to find the two possible solutions for $x$ .

STEP 4

The first possible solution is when $x$ itself is positive or zero, so $x = 9$ .

STEP 5

The second possible solution is when $x$ is negative, so $x = -9$ .
Therefore, the two solutions for the equation $|x| = 9$ are $x = 9$ and $x = -9$ .

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