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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

Review 4.6-4.7


Review 4 6 4 7

Solve each equation or inequality

1.

2.

Multiply every term by 12

b = 2, -5


Review 4 6 4 7

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

Example: Solve.

LCM: 2x

Multiply each fraction through by the LCM

Check your solution!


Solve

Solve.

LCM: ?

LCM: (x+1)

?

Check your solution!

No Solution!


Solve1

Solve.

Factor 1st!

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

Check your solutions!


Example solve1

Example: Solve.

Check your solutions!


Last example solve

Last Example: Solve.

Check your solutions!


Review 4 6 4 7

SolveCheck your solution.

The LCD for the three denominators is

Original equation

Multiply each sideby 24(3 – x).


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6

1

1

1

1

1

Simplify.

Simplify.

Add.


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Check

Original equation

Simplify.

Simplify.

The solution is correct.


Example 6 1e

Solve

Answer:

Example 6-1e


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SolveCheck your solution.

The LCD is

Original equation

p – 1

1

Multiply by the LCD, (p2 – 1).

1

1


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DistributiveProperty

Simplify.

Simplify.

Add(2p2 – 2p + 1)toeach side.


Example 6 2c

Divide eachside by 3.

Factor.

Zero ProductProperty

or

Solve eachequation.

Example 6-2c


Example 6 2d

Check

Original equation

Simplify.

Simplify.

Example 6-2d


Example 6 2e

Original equation

Simplify.

Example 6-2e

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

Answer: The solution is p = 2.


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Solve

Answer:


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Decompose this into partial fractions

5.


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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.


Review 4 6 4 7

Multiply each side by 9s.

Simplify.

Add.

Divide each side by 6.


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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.


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Test

is a solution.


Example 6 5e

Test

is not a solution.

Example 6-5e


Example 6 5f

Test

is a solution.

Example 6-5f


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Answer: The solution


Example 6 5h

Solve

Answer:

Example 6-5h


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Solve each equation or inequality

6.

7.

x = 7

No real solution


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Solve each equation or inequality

8.

9.

k = 7

m = -13


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Solve each equation or inequality

10.

t > 14


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

Upper = 4

Lower = -1


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

12.

13.

x = -0.9, 2.8

x = 1.2


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Approximate the real zeros of each functions

14.

15.

x = -4.4, -0.9, 1.3

No real zeros


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

Pos. 2 or 0

Neg. 1


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17.) Find the possible rational roots:


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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


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20.) Use synthetic division to divide:


Review 4 6 4 7

Graph each equation or inequality:

21.

22.


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Solve each equation or inequality

23.

24.


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Solve each equation by completing the square:

25.

26.


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

Discriminant = 73

2 distinct real roots


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Write the polynomial equation of least degree have the roots:

28.)1, -1, 0.5


Review 4 6 4 7

Find the roots of each equation:

29.

30.


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