Question Find all values of $c$ that satisfy the equation $100=|10c|$ .

Studdy Solution

STEP 1

Assumptions
1. We are given the equation $100 = |10c|$ .
2. We need to solve for all possible values of $c$ .
3. The absolute value function $|x|$ is defined such that $|x| = x$ if $x \geq 0$ and $|x| = -x$ if $x < 0$ .

STEP 2

We will consider two cases for the absolute value function: one where $10c$ is non-negative and one where $10c$ is negative.

STEP 3

Case 1: When $10c$ is non-negative, the absolute value function gives us $|10c| = 10c$ .

STEP 4

Now we solve the equation $100 = 10c$ for $c$ when $10c$ is non-negative.
$100 = 10c$

STEP 5

Divide both sides of the equation by 10 to isolate $c$ .
$\frac{100}{10} = \frac{10c}{10}$

STEP 6

Simplify the equation to find the value of $c$ for Case 1.
$c = 10$

STEP 7

Case 2: When $10c$ is negative, the absolute value function gives us $|10c| = -10c$ .

STEP 8

Now we solve the equation $100 = -10c$ for $c$ when $10c$ is negative.
$100 = -10c$

STEP 9

Divide both sides of the equation by -10 to isolate $c$ .
$\frac{100}{-10} = \frac{-10c}{-10}$

STEP 10

Simplify the equation to find the value of $c$ for Case 2.
$c = -10$

STEP 11

Combining the results from both cases, we find that the values of $c$ that satisfy the equation $100 = |10c|$ are $c = 10$ and $c = -10$ .
The solution in simplest form is $c = 10$ and $c = -10$ .

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