Post on 12-Jan-2016
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Review 4.6-4.7
Solve each equation or inequality
1. 2.
b = 2, -5
Multiply every term by 12
Solve each equation or inequality
3. 4.
w = 2/5, -1USE QUADRATIC FORMULA
What values go on your number lines??
2/5, -1, 0, and 1
Example: Solve.
xx
12
2
13
LCM: 2x
Multiply each fraction through by
the LCM
x
xx
x
x 12*2
2
23*2
246 x
18 x
18xCheck your solution!
18
12
2
1
18
3
1293
Solve.1
54
1
5
xx
x LCM: ?LCM: (x+1)
)1(
)1(5)1(4
)1(
)1(5
x
xx
x
xx
5445 xx
145 xx
1x
Check your solution!
11
54
11
)1(5
0
54
0
5
?
No Solution!
Solve. 14
6
2
232
xx
x
Factor 1st!
1)2)(2(
6
2
23
xxx
x
LCM: (x+2)(x-2)
)2)(2()2)(2(
)2)(2(6
)2(
)2)(2)(23(
xx
xx
xx
x
xxx
42264263 22 xxxxxx
2443 22 xxx
0642 2 xx0322 xx
0)1)(3( xx
01or 03 xx
1or 3 xx
Check your solutions!
Example: Solve.
4
1
4
32
xxx
xx 42 12342 xxx
0122 xx0)3)(4( xx
03or 04 xx3or 4 xx
Check your solutions!
)4(3 x
Last Example: Solve. 1
2
22
62
x
x
xx
)1(6 x)2)(1(2 xxx
6)2(2 xx3)2( xx
0322 xx0)1)(3( xx
01or 03 xx1or 3 xx
1
2
)1(2
6
x
x
xx
Check your solutions!
Solve Check your solution.
The LCD for the three denominators is
Original equation
Multiply each sideby 24(3 – x).
1 1
11 1
6
Simplify.
Simplify.
Add.
Check Original equation
Simplify.
Simplify.
The solution is correct.
Answer:
Solve
Solve Check your solution.
The LCD is
Original equation
Multiply by the LCD, (p2 – 1).
p – 1
1
1
1
DistributiveProperty
Simplify.
Simplify.
Add(2p2 – 2p + 1)to each side.
Factor.
or Zero ProductProperty
Solve eachequation.
Divide eachside by 3.
Check Original equation
Simplify.
Simplify.
Since p = –1 results in a zero in the denominator, eliminate –1.
Answer: The solution is p = 2.
Simplify.
Original equation
Answer:
Solve
Decompose this into partial fractions
5.
Solve
Step 1 Values that make the denominator equal to 0 are excluded from the denominator. For this inequality the excluded value is 0.
Step 2 Solve the related equation.
Related equation
Multiply each side by 9s.
Simplify.
Add.
Divide each side by 6.
Step 3 Draw 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.
is not a solution.
Test
is a solution.
Test
Answer: The solution
Solve
Answer:
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 = 4Lower = -1
Approximate the real zeros of each functions to the nearest tenth.12. 13.
x = 1.2 x = -0.9, 2.8
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 0Neg. 1
17.) Find the possible rational roots:
Find the remainder of each division.Then state whether the binomial is a factor?18. 19.
Remainder = 55Not a factor
Remainder = 18Not a factor
20.) Use synthetic division to divide:
Graph each equation or inequality:
21. 22.
Solve each equation or inequality23. 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 = 732 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.