# 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 92RE
To determine

Expert Solution

## Answer to Problem 92RE

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 number and if multiplied or divided each side by a negative number, then the inequality symbol must be reversed.

The inequality can be solved as follows:

5x3x24x+4<05(x+2)(x2)(x1)<0(x+2)<0,(x2)<0,(x1)<0x<2,x<2,x>1

The solution using interval notation is (,2)(1,2) .

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

### Explanation of Solution

Given information:

The given inequality is 5x3x24x+4<0 .

Formula used:

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

• Add the same quantity to each side of the 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.

Calculation:

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

• Add the same quantity to each side of the 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:

5x3x24x+4<05(x+2)(x2)(x1)<0(x+2)<0,(x2)<0,(x1)<0x<2,x<2,x>1

The solution using interval notation is (,2)(1,2) .

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

Calculation:

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

• Add the same quantity to each side of the 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:

5x3x24x+4<05(x+2)(x2)(x1)<0(x+2)<0,(x2)<0,(x1)<0x<2,x<2,x>1

The solution using interval notation is (,2)(1,2) .

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

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