Solve the equation. |x-5|+4=12

Name: Problem 25, Chapter 1: Algebra and Trigonometry
Uploaded: 2021-06-16T13:10:39-08:00
Duration: 1 min 5 s
Channel: Julie Silva
Description: Solve the equation. |x-5|+4=12

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Key Concepts

Solving Linear Equations

After decomposing the absolute value equation into separate cases, each case results in a linear equation. Solving these linear equations involves standard algebraic techniques, such as isolating the variable by performing operations like addition, subtraction, multiplication, or division.

Case Analysis

Since the absolute value represents a non-negative outcome regardless of the sign of the original expression, an equation involving an absolute value typically leads to two cases: one where the expression inside the absolute value is positive and equals the given number, and one where it is negative and equals the negative of the given number. This duality ensures that all possible solutions are considered.

Absolute Value

The absolute value of a number is its non-negative magnitude, irrespective of its sign. It represents the distance of the number from zero on a number line, making it a measure of magnitude without direction.

Isolation of the Absolute Value Expression

When solving equations that include an absolute value, the first step is often to isolate the absolute value expression on one side of the equation. This manipulation simplifies the process by allowing the equation to be rewritten in a form where the absolute value expression is set equal to a numerical value.

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