Solve Inequality!!!!!!!!!!!!!!!!!!

Question

Given inequality 

  3 >= (4/(x-1)) -(4/(x+2))

Answer 1

3 > [4/(x-1)] - [4/(x+2)]

Rewrite the expression with common denominator

3 > [4(x+2)] - 4(x-1)] / [(x-1)(x+2)]

Multiply each side by (x-1)(x+2).

3 (x-1)(x+2) > [4(x+2)] - 4(x-1)]

Take out common term 4.

3 (x-1)(x+2) > 4 [x+2 - x+1]

3 (x-1)(x+2) > 4 [3 ]

Divide each side by 3.

(x-1)(x+2) > 4

Subtract 4 from each side.

(x-1)(x+2) - 4 > 0

x² + 2x - x - 2 - 4 > 0

x² + x - 6 > 0

Now solve the factor method.

x² + 3x - 2x - 6 > 0

x(x+3)-2(x+3) > 0

Take out common factors.

(x - 2)(x + 3) > 0

(x - 2) > 0 or (x + 3) > 0

consider (x - 2) > 0

Add 2 to each side.

x > 2

consider (x + 3) > 0

Subtract 3 from each side.

x > - 3

There fore x > 2 and x > - 3

graph the solution on number line.

Comments

Solution of the inequality is

x  ≤ -3

-2 < x  < 1

x  ≥ 2.

Answer 2

The inequality is

• Step - 1

State the exclude values,These are the values for which denominator is zero.

The exclude values of the inequality are 1 and -2.

• Step - 2

Solve the related equation

Solutions of related equation x  = -3 and x = 2.

• Step - 3

Draw the vertical lines at the exclude values and at the solutions to separate the number line into intervals.

Answer 3

Continuous...

• Step - 4

Now test  sample values in each interval to determine whether values in the interval satisify the inequality.

Test x  = -4

Above statement is true.

Test  x  = -2.5

Above statement is false.

Test x  = 0

Above statement is true.

Test x  = 1.5

Above statement is false.

Test x  = 3

Above statement is true.

Test x  = -3

Above statement is true.

Test x  = 2

Above statement is true.

The statement is true for x  = -4, x = 0 , x = -3 and x  = 2.

Numberline graph

Solution x  ≤ -3

-2 < x  < 1

x  ≥ 2.