Question

Solve the equation. $$|x-1.2|-2=5$$

   Solve the equation.
$$|x-1.2|-2=5$$

Algebra 1

Ron Larson, Laurie… 1st Edition

Chapter 6, Problem 38

Instant Answer

Solved by Expert Suman Saurav Thakur

09/04/2020

Step 1

We do this by adding 2 to both sides of the equation: $$|x-1.2|-2+2=5+2$$ which simplifies to: $$|x-1.2|=7$$ Show more…

Show all steps

lock

Thanks for your feedback!

Solve the equation. $$|x-1.2|-2=5$$

Play audio

Feedback

Powered by NumerAI

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

Case Analysis

After isolating an absolute value expression, the equation |A| = B, where B is non-negative, is interpreted as having two possible cases: A = B and A = -B. This bifurcation accounts for the fact that both a positive and a negative value yield the same absolute value.

Linear Equation Solving

Once the absolute value expression has been replaced with two separate cases, each case usually results in a linear equation. Solving these linear equations involves using basic algebraic operations to isolate the variable and find the solution.

Absolute Value

Absolute value represents the distance of a number from zero on the number line, regardless of its sign. It is defined such that for any real number x, |x| equals x if x is non-negative and -x if x is negative.

Isolating the Absolute Value Expression

In solving an equation involving an absolute value, the first step is typically to manipulate the equation so that the absolute value expression is isolated on one side. This simplifies the process of applying the definition of absolute value by clearly identifying the quantity being measured.

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