Chapter 2: Q. 642 (page 222)

In the following exercises, solve each inequality, graph the solution in 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 answer is $x \leq 14, x \geq 0$ and the required graphs are

The solution in interval notation is $(- \infty, \infty)$

Step by step solution

Step 1. Given Information

The given inequalities are $\frac{1}{2} x - 3 \leq 4 o r \frac{1}{3} (x - 6) \geq - 2$

Step 2. Calculation

On Solving both the inequalities, we get,

$\frac{x}{2} - 3 \leq 4 \Rightarrow \frac{x}{2} \leq 7 \Rightarrow x \leq 14 \frac{x - 6}{3} \geq - 2 \Rightarrow x - 6 \geq - 6 \Rightarrow x \geq 0$

Step 3. Draw

Draw each solution on the number line.

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

Numbers that satisfy either of inequalities are $- \infty < x < \infty$

Step 4. Interval notation

On writing the solution in interval notation, we get,

$(- \infty, \infty)$

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In the following exercises, solve each inequality, graph the solution in 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

Step 4. Interval notation

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In the following exercises, solve each inequality, graph the solution in 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

Step 4. Interval notation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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