Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 23, 2024

Find the real numbers $x$ that satisfy the equation $|x| = 25.8$ .

STEP 1

Assumptions
1. We are looking for real numbers that satisfy the equation.
2. The absolute value function is defined as $|x| = x$ if $x \geq 0$ and $|x| = -x$ if $x < 0$ .

STEP 2

The absolute value equation can be split into two separate equations, one for the positive case and one for the negative case.
$|x| = 25.8$
This gives us:
1. $x = 25.8$ when $x \geq 0$
2. $-x = 25.8$ when $x < 0$

STEP 3

Solve the first equation where $x$ is non-negative.
$x = 25.8$
Since $25.8$ is a non-negative number, this is a valid solution.

STEP 4

Solve the second equation where $x$ is negative.
$-x = 25.8$
Multiply both sides by $-1$ to isolate $x$ .
$x = -25.8$
Since $-25.8$ is a negative number, this is also a valid solution.

STEP 5

Combine the solutions from STEP_3 and STEP_4.
The real numbers that satisfy the equation $|x| = 25.8$ are $x = 25.8$ and $x = -25.8$ .

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