Chapter 2: Q. 640 (page 222)

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. $\frac{3}{4} x - 5 \geq - 2 a n d - 3 (x + 1) \geq 6$

Short Answer

Expert verified

The required solution is $x \geq 4, x \leq - 3$ .

The required graph is

and there is no solution.

Step by step solution

Step 1. Given Information

The given inequalities are $\frac{3}{4} x - 5 \geq - 2 a n d - 3 (x + 1) \geq 6$

Step 2. Calculation

On solving each inequality,

$\frac{3}{4} x - 5 \geq - 2 \Rightarrow \frac{3}{4} x \geq 3 \Rightarrow x \geq 4 - 3 (x + 1) \geq 6 \Rightarrow x + 1 \leq - 2 \Rightarrow x \leq - 3$

Step 3. Draw

On drawing each solution on the number line,

Now, we will graph the numbers that make both the inequalities true.

There is no number that satisfy both inequalities. Hence, there is no solution.

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In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. $\frac{3}{4} x - 5 \geq - 2 a n d - 3 (x + 1) \geq 6$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Draw

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In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. 34x-5≥-2and-3(x+1)≥6

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Calculation

Step 3. Draw

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Decision Maths

Discrete Mathematics

Geometry

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each inequality, graph the solution on the number line, and write the solution in interval notation. $\frac{3}{4} x - 5 \geq - 2 a n d - 3 (x + 1) \geq 6$