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Review 4.6-4.7 PowerPoint PPT Presentation


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Review 4.6-4.7. Solve each equation or inequality. 1. 2. Multiply every term by 12. b = 2, -5. Solve each equation or inequality. 3. 4. USE QUADRATIC FORMULA. w = 2/5, -1. What values go on your number lines??. 2/5, -1, 0, and 1. Example : Solve. LCM : 2x

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Review 4.6-4.7

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Review 4.6-4.7


Solve each equation or inequality

1.

2.

Multiply every term by 12

b = 2, -5


Solve each equation or inequality

3.

4.

USE QUADRATIC FORMULA

w = 2/5, -1

What values go on your number lines??

2/5, -1, 0, and 1


Example: Solve.

LCM: 2x

Multiply each fraction through by the LCM

Check your solution!


Solve.

LCM: ?

LCM: (x+1)

?

Check your solution!

No Solution!


Solve.

Factor 1st!

LCM: (x+2)(x-2)

Check your solutions!


Example: Solve.

Check your solutions!


Last Example: Solve.

Check your solutions!


SolveCheck your solution.

The LCD for the three denominators is

Original equation

Multiply each sideby 24(3 – x).


6

1

1

1

1

1

Simplify.

Simplify.

Add.


Check

Original equation

Simplify.

Simplify.

The solution is correct.


Solve

Answer:

Example 6-1e


SolveCheck your solution.

The LCD is

Original equation

p – 1

1

Multiply by the LCD, (p2 – 1).

1

1


DistributiveProperty

Simplify.

Simplify.

Add(2p2 – 2p + 1)toeach side.


Divide eachside by 3.

Factor.

Zero ProductProperty

or

Solve eachequation.

Example 6-2c


Check

Original equation

Simplify.

Simplify.

Example 6-2d


Original equation

Simplify.

Example 6-2e

Since p = –1 results in a zero in the denominator, eliminate –1.

Answer: The solution is p = 2.


Solve

Answer:


Decompose this into partial fractions

5.


Solve

Related equation

Step 1Values that make the denominator equal to 0 are excluded from the denominator.For this inequality the excluded value is 0.

Step 2Solve the related equation.


Multiply each side by 9s.

Simplify.

Add.

Divide each side by 6.


Step 3Draw vertical lines at the excluded value and at the solution to separate the number line into regions.

Now test a sample value in each region to determine if the values in the region satisfy the inequality.


Test

is a solution.


Test

is not a solution.

Example 6-5e


Test

is a solution.

Example 6-5f


Answer: The solution


Solve

Answer:

Example 6-5h


Solve each equation or inequality

6.

7.

x = 7

No real solution


Solve each equation or inequality

8.

9.

k = 7

m = -13


Solve each equation or inequality

10.

t > 14


11.) Find the upper and lower bound of the zeros of:

Upper = 4

Lower = -1


Approximate the real zeros of each functions to the nearest tenth.

12.

13.

x = -0.9, 2.8

x = 1.2


Approximate the real zeros of each functions

14.

15.

x = -4.4, -0.9, 1.3

No real zeros


16.) Find the number of positive, negative, and imaginary:

Pos. 2 or 0

Neg. 1


17.) Find the possible rational roots:


Find the remainder of each division.

Then state whether the binomial is a factor?

18.

19.

Remainder = 55

Not a factor

Remainder = 18

Not a factor


20.) Use synthetic division to divide:


Graph each equation or inequality:

21.

22.


Solve each equation or inequality

23.

24.


Solve each equation by completing the square:

25.

26.


27.) Find the discriminant of the function given and describe the nature of the roots.

Discriminant = 73

2 distinct real roots


Write the polynomial equation of least degree have the roots:

28.)1, -1, 0.5


Find the roots of each equation:

29.

30.


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