Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 17, 2024

Find the value of $y$ when $x$ is -9, given the equation $y=|x|+12$ .

STEP 1

Assumptions
1. The function given is $y = |x| + 12$
2. The value of $x$ is given as $-9$

STEP 2

The absolute value function $|x|$ is defined as the distance of $x$ from zero on the number line, which is always non-negative.

STEP 3

If $x$ is negative, then $|x|$ is the negation of $x$ , which makes it positive. If $x$ is positive, $|x|$ is equal to $x$ itself.

STEP 4

Since $x$ is given as $-9$ , which is negative, we will negate $x$ to find $|x|$ .

STEP 5

Calculate the absolute value of $x$ .
$|x| = |-9|$

STEP 6

Negate $x$ to get the absolute value.
$|x| = 9$

STEP 7

Now that we have $|x|$ , we can substitute it into the function to find $y$ .
$y = |x| + 12$

STEP 8

Substitute $|x| = 9$ into the function.
$y = 9 + 12$

STEP 9

Calculate the value of $y$ .
$y = 21$
The value of $y$ when $x$ is $-9$ is $21$ .

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