equations
Solve.
9 = -9 - m
9 = -9 - m
18 = -m
-18 = m
A polynomial that is only a singular term with no degree is called...
A constant monomial
h / -7 < 1/5
What is the solution? Graph it.
h / -7 < 1/5
h < -7/5
Open Circle at -7/5 line going to the left
What is the product of -3 and 8, decreased by 6 then halved.
(-3)(8). "product of -3 and 8"
-24 - 6. "decreased by 6"
-30 / 2. "then halved"
-15
Libby biked at a speed of 15km/hr for 25 minutes. How far did she bike? Answer as a fraction OR a decimal.
15km / 60 min = x km / 25 min
60x = 375
60x/60 = 375/60
x = 6 15/60
6 1/4
Libby biked 6.25 or 6 and 1/4 kilometers after 25 minutes
5/2x = x - 1/4
5/2x = x - 1/4
3/2x = -1/4
3x = -1/2
x = -1/6
Classify this based on its degree and number of terms.
2x3yz
A quintic monomial
-m < -12 - 3m
Find the solution and graph.
-m < -12 - 3m
2m < -12
m < -6
Find three consecutive odd integers whose sum is -45
x
x+2
x+4
3x + 6 = -45
3x = -51
x = -17
-17, -15, -13
0.25(1/5 - 1/2)
0.25(1/5 - 1/2)
0.25(2/10 - 5/10)
0.25(-3/10)
1/4 * (-3/10)
-3/40
1/5(50x - 20) - 7x = 8 + 2x
1/5(50x - 20) - 7x = 8 + 2x
10x - 4 - 7x = 8 + 2x
3x - 4 = 8 + 2x
x = 12
Write a polynomial that is a quartic trinomial with no constant term
Answers will vary.
Example correct response: x4 + xyz + x
-4/3x < x + 3
Find the solution and graph.
-4/3x < x + 3
-4x < 3x + 9
-7x < 9
x > -9/7
Open circle at -9/7, line going to the right
Write an inequality and solve.
Tabor has $500. She wants to buy huge bags of candy. Each bag costs $14. What is the maximum number of bags Tabor can buy?
14x < 500
14x/14 < 500/14
x < 35
No more than 35 bags of candy
What is the opposite of the following.
-2(|-3 - 3| - 1) -23
-2(|-3 - 3| - 1) - 23
-2(|-6| -1) - 23
-2(6-1) - 23
-2(5) - 8
-10 - 8
-18
The opposite is 18.
x + 3(-2x - 1) = 5 + 4x
x + 3(-2x - 1) = 5 + 4x
x - 6x - 3 = 5 + 4x
-5x - 3 = 5 + 4x
- 9x = 8
x = -8/9
62 + 8(xy - 1)
Simplify then re-write in standard form. Lastly, classify based on the number of terms and its degree.
62 + 8(xy - 1)
36 + 8xy - 8
28 + 8xy
STANDARD FORM -> 8xy + 28
Quadratic Binomial
2 < 2x < 6
Find solution and graph.
1 < x < 3
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number.
4x + 40 = 100 - x
5x = 60
x = 12
Solve.
7 - 3/2y = y + 4
7 - 3/2y = y + 4
-3/2y = y - 3
-3y = 2y - 6
-5y = -6
y = 6/5
-8 = -2/3(9y - 12) + 2y
-8 = -2/3(9y - 12) + 2y
-8 = -6y + 8 + 2y
-8 = -4y + 8
-16 = -4y
4 = y
Simplify. Re-write in standard form. Classify.
-1/4(24y4 - xy + 28) + 3xy - 1 - z3
-1/4(24y4 - xy + 28) + 3xy - 1 - z3
-6y4 + 1/4xy - 7 + 3xy - 1 - z3
-4y4 - z3 + 13/4xy - 8
A quartic polynomial
Find the solution and graph.
9 + 2b < 7 OR 7 - 5b < -8
b < -1 OR b > 3
Three consecutive integers are such that three times the smallest is 14 more than the largest. Find the integers.
x
x+1
x+2
3x = 14 + x + 2
3x = 16 + x
2x = 16
x = 8
8, 9, 10
Find three consecutive numbers such that three times the smallest and four more than the middle has a sum of -23.
3x + 4 + x + 1 = -23
4x + 5 = -23
4x = -28
x = -7
-7, -6, -5