Chapter 2: Q. 9 (page 126)

Solve the inequality. Graph the solution set.
$|4 x + 1| \geq 7$

Short Answer

Expert verified

The solution set of the given inequality is:

$(- \infty, - 2] \cup [\frac{3}{2}, \infty)$

The graph of the solution set is given as:

Step by step solution

Step 1. Given information

The given inequality is $|4 x + 1| \geq 7$

Step 2. Open the modulus function

We know that, from the principle of absolute value, for $|x| \geq a$ , we have:

$- a \geq x \geq a$ .

Similarly, for $|4 x + 1| \geq 7$ , we have:

$- 7 \geq 4 x + 1 \geq 7$

Step 3. Solving the inequality

Solving the inequality using properties, we get :

$- 7 \geq 4 x + 1 \geq 7 - 7 - 1 \geq 4 x \geq 7 - 1 - 8 \geq 4 x \geq 6 - 2 \geq x \geq \frac{3}{2}$

Step 4. Verify the solution set

Substituting $x = 2$ in the given inequality, we get:

$|4 x + 1| \geq 7 |4 \times (- 2) + 1| \geq 7 |- 8 + 1| \geq 7 |- 7| \geq 7 7 \geq 7$

This is true.

Hence, the solution set of the given inequality is $- 2 \geq x \geq \frac{3}{2}$ or $x \leq - 2 o r x \geq \frac{3}{2}$

Step 5. Graph the solution set

The graph of the solution set is given as:

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Solve the inequality. Graph the solution set.
$|4 x + 1| \geq 7$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Open the modulus function

Step 3. Solving the inequality

Step 4. Verify the solution set

Step 5. Graph the solution set

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Solve the inequality. Graph the solution set.4x+1≥7

Short Answer

Step by step solution

Step 1. Given information

Step 2. Open the modulus function

Step 3. Solving the inequality

Step 4. Verify the solution set

Step 5. Graph the solution set

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve the inequality. Graph the solution set.
$|4 x + 1| \geq 7$