Question

Solve each equation. Check your solutions. $$ -4|d+2|=-12 $$

   Solve each equation. Check your solutions.
$$
-4|d+2|=-12
$$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 5, Problem 91

Instant Answer

Solved by Expert Ankit Gupta

04/06/2020

Step 1

Step 1: First, we divide the equation by -4 to isolate the absolute value: $$ |d+2| = \frac{-12}{-4} = 3 $$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve each equation. Check your solutions. $$ -4|d+2|=-12 $$

Play audio

Feedback

Powered by NumerAI

Ankit Gupta and 69 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Splitting into Two Cases

Once the absolute value expression is isolated, the equation is split into two separate equations based on the definition of absolute value. This means setting the expression inside equal to the positive and negative of the isolated value. Each case is then solved for the variable.

Checking Solutions

After obtaining potential solutions, it is important to substitute them back into the original equation to verify that they actually satisfy the equation. The checking process confirms that no extraneous solutions were introduced during the process of isolating the absolute value or splitting into cases.

Absolute Value Equation

An absolute value equation is one where the variable appears inside an absolute value expression. The absolute value of an expression represents its non-negative distance from zero on the number line. When solving such equations, the expression within the absolute value is set equal to the positive value or its negative counterpart after isolating the absolute value term.

Isolation of the Absolute Value Term

A key step in solving absolute value equations, especially when there is an external coefficient, is to isolate the absolute value expression on one side of the equation. This might involve dividing or multiplying both sides of the equation by a constant, ensuring that the solution process is valid by keeping track of sign changes and potential restrictions.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later