Question

Solve each absolute value equation. $|2 x|-6=4$

   Solve each absolute value equation.
$|2 x|-6=4$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Elayn Martin-Gay 4th Edition

Chapter 9, Problem 12

Instant Answer

Solved by Expert Ali Soave

03/13/2020

Step 1

We do this by adding 6 to both sides of the equation. This gives us: \[|2x| = 4 + 6\] Show more…

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Solve each absolute value equation. $|2 x|-6=4$

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Key Concepts

Absolute Value

The absolute value of a number represents its distance from zero on the number line, always resulting in a nonnegative value. It captures the idea of magnitude without regard to direction, which is why when an equation involves an absolute value, it generally implies two possible cases for the expression inside the absolute value.

Isolating the Absolute Value Expression

A fundamental step in solving absolute value equations is isolating the absolute value term. This manipulation arranges the equation into a form such as |expression| = constant, which is essential for applying further techniques to consider the solution scenarios.

Splitting into Cases

Once the absolute value expression is isolated, the equation |expression| = constant (with constant nonnegative) can be split into two separate equations: one where the expression equals the constant, and one where it equals the negative of the constant. This case analysis leverages the definition of absolute value and is key to finding all valid solutions of the equation.

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