Chapter 2: Q. 2.138 (page 199)

Solve $|4 x - 3| - 5 = 2$

Short Answer

Expert verified

The required solutions are $x_{1} = - 1, x_{2} = \frac{5}{2}$ .

Step by step solution

Step 1. Given information.

We have:

$|4 x - 3| - 5 = 2$

Step 2. Isolate the absolute expression.

We have:

$|4 x - 3| - 5 = 2$

Add $5$ to both sides:

$|4 x - 3| - 5 + 5 = 2 + 5 |4 x - 3| = 7$

Step 3. Write the equivalent equations.

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

$4 x - 3 = - 7 or 4 x - 3 = 7$

Step 4. Solve the each equations.

Start with first equation:

$4 x - 3 = - 7$

Add $3$ to both sides:

$4 x - 3 + 3 = - 7 + 3 4 x = - 4 \frac{4 x}{4} = \frac{- 4}{4} x = - 1$

Now, solve the second equation:

$4 x - 3 = 7$

Add $3$ to both sides:

$4 x - 3 + 3 = 7 + 3 4 x = 10 \frac{4 x}{4} = \frac{10}{4} x = \frac{5}{2}$

Step 5. Check the each solution.

Substitute $- 1$ and $\frac{5}{2}$ into the original equation:

$|4 x - 3| - 5 = 2$

At $x = - 1$ :

$|4 (- 1) - 3| - 5 = 2 7 - 5 = 2 2 = 2$

Hence, verified.

At $x = \frac{5}{2}$ :

$|4 (\frac{5}{2}) - 3| - 5 = 2 7 - 5 = 2 2 = 2$

Hence, verified.

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Solve $|4 x - 3| - 5 = 2$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Isolate the absolute expression.

Step 3. Write the equivalent equations.

Step 4. Solve the each equations.

Step 5. Check the each solution.

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Solve4x-3-5=2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Isolate the absolute expression.

Step 3. Write the equivalent equations.

Step 4. Solve the each equations.

Step 5. Check the each solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

Solve $|4 x - 3| - 5 = 2$