Problem 449 Solve. $$ \left|\frac{3}{5} ... [FREE SOLUTION]

Chapter 2: Problem 449

Solve. $$ \left|\frac{3}{5} x-2\right|+5=2 $$

Short Answer

Expert verified

No solution.

Step by step solution

Isolate the absolute value expression

Subtract 5 from both sides of the equation to isolate the absolute value expression: \[ \left|\frac{3}{5} x-2\right| + 5 - 5 = 2 - 5 \] This simplifies to: \[ \left| \frac{3}{5} x-2 \right| = -3 \]

Analyze the absolute value result

Recognize that an absolute value expression equals a negative number is impossible. Since $ \left| \frac{3}{5} x-2 \right| = -3 $ suggests an absolute value equal to negative, there is no solution.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

isolating absolute value

To solve an absolute value equation, the first step is to isolate the absolute value expression. In our exercise, we start with the equation:
$$\begin{array}{c} \bigg|\frac{3}{5}x - 2\bigg| + 5 = 2 \ \text{Step 1: Subtract 5 from both sides:} \ \bigg|\frac{3}{5}x - 2\bigg| + 5 - 5 = 2 - 5 \ \bigg|\frac{3}{5}x - 2\bigg| = -3 \ \text{Now, the absolute value is isolated in the equation:} \ \bigg|\frac{3}{5}x - 2\bigg| = -3 \end{array}$$ It's important to always complete this step first since it makes the equation much simpler to handle.

impossibility of negative absolute value

In the context of absolute values, it is crucial to understand that the absolute value of any number is always non-negative. This means absolute value can never be negative. Absolute values measure the distance of a number from zero, which is always a positive number or zero.
Now, in our exercise, we end up with: $$ \bigg|\frac{3}{5}x - 2\bigg| = -3$$. But, by definition, an absolute value cannot equal a negative number. This indicates something is off with our equation. Hence, admitting that an absolute value expression cannot be negative is essential to identifying that an equation holds no solutions.

solving absolute value equations

Typically, solving an absolute value equation involves creating two separate equations, since $\big|A\big| = B$ can split into $A = B$ and $A = -B$. However, in our given exercise, we notice an immediate problem: $\big| \big|\frac{3}{5} x - 2\big| = -3 \big| \big|$. Since we know absolute values can't be negative, we conclude the equation has no solutions right away. \[Sub-Headline: General Steps for Solving:
- Isolate the absolute value on one side.
- Split into two possible equations.
- Solve each equation separately. \]
Be sure always to check your solutions in the context of the original absolute value problem to avoid errors.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Solve. $$ \left|\frac{3}{5} x-2\right|+5=2 $$

Short Answer

Step by step solution

Isolate the absolute value expression

Analyze the absolute value result

Key Concepts

isolating absolute value

impossibility of negative absolute value

solving absolute value equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Calculus

Discrete Mathematics

Geometry

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.