Chapter 2: Q. 2.144 (page 202)

Solve: $|6 x - 5| = |3 x + 4|$

Short Answer

Expert verified

The required solutions are $x_{1} = \frac{1}{9}, x_{2} = 3$ .

Step by step solution

Step 1. Given information.

We have:

$|6 x - 5| = |3 x + 4|$

Step 2. Write the equivalent equations.

We have:

$|6 x - 5| = |3 x + 4|$

Write the inequality as $(6 x - 5) = - (3 x + 4)$ or $(6 x - 5) = (3 x + 4)$ .

Step 3. Solve the each equations.

Start with first equation:

$(6 x - 5) = - (3 x + 4)$

$6 x - 5 = - 3 x - 4 6 x - 5 + 5 = - 3 x - 4 + 5 6 x = - 3 x + 1 6 x + 3 x = - 3 x + 1 + 3 x 9 x = 1 x = \frac{1}{9}$

Now, solve the second equation:

$(6 x - 5) = (3 x + 4)$

$6 x - 5 + 5 = 3 x + 4 + 5 6 x = 3 x + 9 6 x - 3 x = 3 x + 9 - 3 x 3 x = 9 \frac{3 x}{3} = \frac{9}{3} x = 3$

Step 4. Check the each solution.

Substitute $\frac{1}{9}$ and $3$ into the original equation:

$|6 x - 5| = |3 x + 4|$

At $x = \frac{1}{9}$ :

$|6 (\frac{1}{9}) - 5| = |3 (\frac{1}{9}) + 4| \frac{13}{3} = \frac{13}{3}$

At $x = 3 :$

$|6 (3) - 5| = |3 (3) + 4| 13 = 13$

Hence, verified.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Solve: $|6 x - 5| = |3 x + 4|$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equivalent equations.

Step 3. Solve the each equations.

Step 4. Check the each solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve:6x-5=3x+4

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the equivalent equations.

Step 3. Solve the each equations.

Step 4. Check the each solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Solve: $|6 x - 5| = |3 x + 4|$