Chapter 4: Q. 42 (page 246)

Solve each inequality. Graph the solution set.
$\frac{6}{x + 3} \geq 1$

Short Answer

Expert verified

The real zeroes are 3 and $- 3$ and the solution set can be graphed as

Step by step solution

Step 1. Given Information

The given inequality is $\frac{6}{x + 3} \geq 1$

Step 2. Calculation

Solve the given inequality as follows,

$\frac{6}{x + 3} - 1 \geq 1 - 1 \frac{6}{x + 3} - 1 \geq 0 \frac{6}{x + 3} - 1 (\frac{x + 3}{x + 3}) \geq 0 \frac{- x + 3}{x + 3} \geq 0$

Now, let $f (x) = \frac{- x + 3}{x + 3}$ . We will find the real zeroes of the numerator and denominator.

$- x + 3 = 0 \Rightarrow x = 3 x + 3 = 0 \Rightarrow x = - 3$

Thus, real zeroes of the function are $- 3 a n d 3$

Step 3. Graph

Construct the table by using a number from each interval to check whether the function is positive or negative.

Thus, the solution set is $\{x | - 3 < x \leq 3\}$

And the solution set can be graphed as

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Solve each inequality. Graph the solution set.
$\frac{6}{x + 3} \geq 1$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Graph

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Solve each inequality. Graph the solution set.6x+3≥1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Pure Maths

Probability and Statistics

Logic and Functions

Statistics

Study anywhere. Anytime. Across all devices.

Solve each inequality. Graph the solution set.
$\frac{6}{x + 3} \geq 1$