Chapter 2: Q. 5 (page 126)

Find the real solutions of the equation:
$|2 x + 3| = 4$

Short Answer

Expert verified

The solution of the equation is :

$x = \frac{1}{2} x = \frac{- 7}{2}$

Step by step solution

Step 1. Given information

The given equation is $|2 x + 3| = 4$

Step 2. Open the modulus function

We know that, for $|x| = a$ , we have:

$x = a x = - a$

Similarly, for $|2 x + 3| = 4$ , we have:

$2 x + 3 = 4 2 x + 3 = - 4$

Step 3. Solving the equations

Solving the equation $2 x + 3 = 4$ , we get:

$2 x + 3 = 4 2 x = 4 - 3 2 x = - 1 x = - \frac{1}{2}$

Solving the equation $2 x + 3 = - 4$ , we get:

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

Step 4. Verify the solutions

Substituting $x = \frac{1}{2}$ in the given equation, we get:

$|2 x + 3| = 4 |2 \times \frac{1}{2} + 3| = 4 |1 + 3| = 4 |4| = 4 4 = 4$

This is true.

Substituting $x = - \frac{7}{2}$ in the given equation, we get:

$|2 x + 3| = 4 |2 \times (- \frac{7}{2}) + 3| = 4 |- 7 + 3| = 4 |- 4| = 4 4 = 4$

This is true.

Thus, the solution of the equation is

x = \frac{1}{2} x = - \frac{7}{2}

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Find the real solutions of the equation:
$|2 x + 3| = 4$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Open the modulus function

Step 3. Solving the equations

Step 4. Verify the solutions

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Find the real solutions of the equation:2x+3=4

Short Answer

Step by step solution

Step 1. Given information

Step 2. Open the modulus function

Step 3. Solving the equations

Step 4. Verify the solutions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Theoretical and Mathematical Physics

Calculus

Statistics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the real solutions of the equation:
$|2 x + 3| = 4$