Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 19, 2024

Find the solutions to the absolute value equation $|x| + 10 = 1$ .

STEP 1

Assumptions
1. The equation is $|x| + 10 = 1$ .
2. We need to find all values of $x$ that satisfy the equation.

STEP 2

First, we need to isolate the absolute value expression on one side of the equation. To do this, we can subtract 10 from both sides of the equation.
$|x| + 10 - 10 = 1 - 10$

STEP 3

Simplify both sides of the equation to get the absolute value by itself.
$|x| = -9$

STEP 4

Recognize that the absolute value of a number is always non-negative. Therefore, there are no real numbers $x$ such that $|x| = -9$ , since the absolute value cannot equal a negative number.

STEP 5

Conclude that there are no real solutions to the equation $|x| + 10 = 1$ because the absolute value of $x$ cannot be a negative number.
The equation $|x| + 10 = 1$ has no solution.

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