Chapter 1: Q60. (page 39)

Solve each equation. Check the solution.
If $8 |4 x - 3| = 64$

Short Answer

Expert verified

The value of $x$ is $2.75$ and $- 1.25$ .

Step by step solution

- State the definition of absolute value.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

- Solve the inequality.

If x is a number, then absolute value of x is written as $|x|$ .

Here, the inequality is:

$8 |4 x - 3| = 64$

Case 1:

\begin{matrix} a = b \\ 8 (4 x - 3) = 64 \\ 32 x - 24 = 64 \\ 32 x - 24 + 24 = 64 + 24 \\ 32 x = 88 \\ x = 2.75 \end{matrix}

Or Case 2:

\begin{matrix} a = - b \\ 8 (4 x - 3) = - 64 \\ 32 x - 24 = - 64 \\ 32 x - 24 + 24 = - 64 + 24 \\ 32 x = - 40 \\ x = - 1.25 \end{matrix}

The solution is $2.75$ and $- 1.25$

- Check the solution.

For case 1: $x = 2.75$ .

Check:

\begin{array}{r} 8 |4 x - 3| = 64 \\ 8 |(4 \times 2.75) - 3| = 64 \\ 8 |11 - 3| = 64 \\ 8 |8| = 64 \\ 8 \times 8 = 64 \\ 64 = 64 \end{array}

Thus, it is correct.

For case 2: $x = - 1.25$ .

Check:

\begin{array}{r} 8 |4 x - 3| = 64 \\ 8 |(4 \times - 1.25) - 3| = 64 \\ 8 |- 5 - 3| = 64 \\ 8 |- 8| = 64 \\ 8 \times 8 = 64 \\ 64 = 64 \end{array}

Thus, it is also correct.

- State the conclusion.

Therefore, the solution set for x is $\{2.75, - 1.25\}$ .

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Solve each equation. Check the solution.
If $8 |4 x - 3| = 64$

Short Answer

Step by step solution

- State the definition of absolute value.

- Solve the inequality.

- Check the solution.

- State the conclusion.

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Solve each equation. Check the solution.If 84x-3=64

Short Answer

Step by step solution

- State the definition of absolute value.

- Solve the inequality.

- Check the solution.

- State the conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Applied Mathematics

Statistics

Pure Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve each equation. Check the solution.
If $8 |4 x - 3| = 64$