Chapter 2: Q. 2.143 (page 202)

Solve: $|7 x - 3| = |3 x + 7|$

Short Answer

Expert verified

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

Step by step solution

Step 1. Given Information.

We have:

$|7 x - 3| = |3 x + 7|$

Step 2. Write the equivalent equations.

We have:

$|7 x - 3| = |3 x + 7|$

Write the inequality as $(7 x - 3) = - (3 x + 7)$ or $(7 x - 3) = (3 x + 7)$ .

Step 3. Solve each equation.

Start with first equation:

$(7 x - 3) = - (3 x + 7)$

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

Now, solve the second equation:

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

Step 4. Check the each solution.

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

$|7 x - 3| = |3 x + 7|$

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

$|7 (- \frac{2}{5}) - 3| = |3 (- \frac{2}{5}) + 7| \frac{29}{5} = \frac{29}{5}$

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

$|7 (\frac{5}{2}) - 3| = |3 (\frac{5}{2}) + 7| \frac{29}{2} = \frac{29}{2}$

Hence, verified.

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Solve: $|7 x - 3| = |3 x + 7|$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the equivalent equations.

Step 3. Solve each equation.

Step 4. Check the each solution.

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Solve:7x-3=3x+7

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Write the equivalent equations.

Step 3. 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

Probability and Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve: $|7 x - 3| = |3 x + 7|$