Chapter 2: Q. 2.137 (page 200)

Solve $|3 x - 5| - 1 = 6$

Short Answer

Expert verified

The required solutions are $x_{1} = - \frac{2}{3}, x_{2} = 4$ .

Step by step solution

Step 1. Given information.

We have:

$|3 x - 5| - 1 = 6$

Step 2. Isolate the absolute value expression

We have:

$|3 x - 5| - 1 = 6$

Add $1$ to both sides:

$|3 x - 5| - 1 + 1 = 6 + 1 |3 x - 5| = 7$

Step 4. Solve each equation

Apply absolute rule: $If | u | = a, a > 0 then u = a or u = - a$

First, solve $3 x - 5 = - 7 :$

Add $5$ to both sides:

$3 x - 5 + 5 = - 7 + 5 3 x = - 2 \frac{3 x}{3} = \frac{- 2}{3} x = - \frac{2}{3}$

Now, solve the second equation:

$3 x - 5 = 7$

Add $5$ to both sides:

$3 x - 5 + 5 = 7 + 5 3 x = 12 \frac{3 x}{3} = \frac{12}{3} x = 4$

Step 4. Check the each solution

Substitute $- \frac{2}{3}$ and $4$ into the original equation::

$|3 x - 5| - 1 = 6$

At $x = - \frac{2}{3} :$

$|3 (- \frac{2}{3}) - 5| - 1 = 6 7 - 1 = 6 6 = 6$

Hence, verified.

At $x = 4 :$

$|3 (4) - 5| - 1 = 6 7 - 1 = 6 6 = 6$

Hence, verified.

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Solve $|3 x - 5| - 1 = 6$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Isolate the absolute value expression

Step 4. Solve each equation

Step 4. Check the each solution

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Solve3x-5-1=6

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Isolate the absolute value expression

Step 4. Solve each equation

Step 4. Check the each solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Geometry

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Solve $|3 x - 5| - 1 = 6$