# The solution of the given inequality and express the solution using interval notation. Also graph the solution set on the real number line.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 87RE
To determine

## To calculate:The solution of the given inequality and express the solution using interval notation. Also graph the solution set on the real number line.

Expert Solution

Inequalities are mathematical expressions involving the symbols and .

In order to solve an inequality, the following things can be done.

• Add the same number to each side of the inequality.

• Subtract the same number from each side .

• Multiply or divide each side by the same numberand if multiplied or divided each side by a negative number, then the inequality symbol must be reversed.

The inequality can be solved as follows:

3x2+11>03x+9>03(x+3)>0(x+3)>0

x>3

The solution using interval notation is (3,)

The shaded region shows solution of the given inequality on the graph below .

### Explanation of Solution

Given information:

The given inequality is 3x2+11>0

Formula used:

In order to solve an inequality, the following things can be done.

• Add the same quantity to each side of th inequality

• Subtract the same quantity from each side

• Multiply or divide each side by the same positive quantity and If multiplied or divided each side by a negative quantity, then the inequality symbol must be reversed.

In case of non linear inequality,the function may be factorised and solved further long division method etc.

The following methods can be used for showing the solutions of the inequalities.

• solve simple inequalities using algebra

• solve simple inequalities by drawing graphs

• solve inequalities in which there is a modulus symbol

Calculation:

In order to solve an inequality, the following things can be done.

• Add the same quantity to each side of th inequality

• Subtract the same quantity from each side

• Multiply or divide each side by the same positive quantity and If multiplied or divided each side by a negative quantity, then the inequality symbol must be reversed.

The inequality can be solved as follows:

3x2+11>03x+9>03(x+3)>0(x+3)>0

x>3

The solution using interval notation is (3,)

The shaded region shows the given inequality on the graph below .

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