Chapter 1: Q44. (page 31)

Solve the equation. Check the solutions.
$| 3 x - 7 | - 5 = - 3$

Short Answer

Expert verified

The values are $x = 3, \frac{5}{3}$ .

Step by step solution

Step 1- Apply the concept of absolute value.

Absolute value describes the distance from zero that a number is on the number line,without considering direction. The absolute value of a number is never negative.

Step 2- Simplify the expression.

Consider the expression $| 3 x - 7 | - 5 = - 3$ .

Add 5 on both sides of the equation as follows:

$\begin{array}{l} | 3 x - 7 | - 5 = - 3 \\ | 3 x - 7 | - 5 + 5 = - 3 + 5 \\ | 3 x - 7 | = 2 \end{array}$

Step 3- Step description.

Apply the absolute rule as follows:

Case 1. When $3 x - 7 = - 2$ .

$\begin{array}{l} 3 x - 7 = - 2 \\ 3 x - 7 + 2 = 0 \\ 3 x - 5 = 0 \\ 3 x = 5 \\ x = \frac{5}{3} \end{array}$

Case 2. When $3 x - 7 = 2$

$\begin{array}{l} 3 x - 7 = 2 \\ 3 x - 7 - 2 = 0 \\ 3 x - 9 = 0 \\ 3 x = 9 \\ x = 3 \end{array}$

Therefore, the value is $x = 3, \frac{5}{3}$ .

Step 4-Verify the solutions.

Substitute $x = 3, \frac{5}{3}$ in the equation $| 3 x - 7 | - 5 = - 3$ and simplify as follows:

$\begin{array}{l} | 3 x - 7 | - 5 = - 3 \\ | 3 (3) - 7 | - 5 = - 3 \\ | 9 - 7 | - 5 = - 3 \\ | 2 | - 5 = - 3 \\ 2 - 5 = - 3 \\ - 3 = - 3 \end{array}$

$\begin{array}{l} | 3 x - 7 | - 5 = - 3 \\ | 3 (\frac{5}{3}) - 7 | - 5 = - 3 \\ | 5 - 7 | - 5 = - 3 \\ | - 2 | - 5 = - 3 \\ 2 - 5 = - 3 \\ - 3 = - 3 \end{array}$

Since the left-hand side and right-hand side is equal in both the cases thus the values are $x = 3, \frac{5}{3}$ .

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Solve the equation. Check the solutions.
$| 3 x - 7 | - 5 = - 3$

Short Answer

Step by step solution

Step 1- Apply the concept of absolute value.

Step 2- Simplify the expression.

Step 3- Step description.

Step 4-Verify the solutions.

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Solve the equation. Check the solutions.|3x-7|-5=-3

Short Answer

Step by step solution

Step 1- Apply the concept of absolute value.

Step 2- Simplify the expression.

Step 3- Step description.

Step 4-Verify the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Applied Mathematics

Pure Maths

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the equation. Check the solutions.
$| 3 x - 7 | - 5 = - 3$