Inequalities
x + 5 >/ 8
x >/ 3
Work:
Subtract 5 from both sides
What is slope intercept form?
y = mx + b
2y + 7x = -5
+ 5y -7x = 12
Solve for y using elimination
y = 1
Work:
2y + 7x = -5
+ 5y -7x = 12
After adding you get: 7y + 0 = 7 (divide both sides by 7)
y = 1
How many terms does a binomial have?
2 terms
Simplify: (x3)4
x12
You multiply the exponents outside the parenthesis with the ones inside.
10x + 5 < 11 - 2x
Solve for x.
x <1/2
Work:
10x + 5 < 11 - 2x
- 5 - 5
12x < 6 (Divide both sides by 12)
x < 1/2
What is standard form?
Ax + By = C
2x+5y=19
y=3x -3
Solve for x and y using substitution
x=2 , y=3
2x+5(3x-3)=19 (substitute)
2x+15x-15=19 (add like terms)
17x=34 (divide 12)
x=2
y=3(2)-3
y=6-3
y=3
How many terms does a polynomial have?
2 or more terms (2 = binomial)
Simplify: (5x3) (4x7)
20x10
Work: (5x3) (4x7) (Multiply 5 and 4)
20x3x7 (Combine like terms: x)
20x10
Solve.
(8^2)x + 1073 < 92x +625
x > 16
Work:
(8^2)x + 1073 < 92x +625
(Start with 8^2 then subtract 625 from each side)
64x + 448 < 92x (subtract 64x from both sides)
448 < 28x (divide both sides by 28)
16 < x
What is point slope form?
y - y1 = m (x - x1)
-2x + y = 4
-2x + 3y = 4
Solve for x and y using elimination
y = 1 and x = -1
Work:
-2x + y = 4
-2x + 3y = 4 (add the two equations)
4y = 8 (divide both sides by 4)
Plug in y = 2 to either equation (we did the -2x + y = 4)
-2x + (2) = 4 (subtract 2 on both sides)
-2x = 2 (divide both sides by -2)
x = -1
(9x-4)(x-6)
Solve for x
x = 4/9, 6
Simplify: (-2x3y4)2
4x6y8
Work:
Distribute the 2 to everything in the parenthesis
-3 (3x + 6) >/ 7 (x - 2)
Solve.
-1/4 >/ x
-3 (3x + 6) >/ 7 (x - 2) (distribute -3 and 7 on both sides)
-9x -18 >/ 7x -14 (add 14)
-9x -4 >/ 7x (add 9x)
-4 >/ 16x (divide both sides by 16)
-1/4 >/ x
y + 7 = 14(x+4)
Solve for y
y=14x + 49
Work: y + 7 = 14(x+4)
(Distribute the 14 to inside the parenthesis)
y + 7 = 14x + 56 (subtract 7 from both sides)
y=14x + 49
3x + 4y = 12
4x - 8y = -12
Solve for x and y by elimination
x = 1.2 and y = 2.1
Work: Multiply both sides of 3x + 4y = 12 to get -
6x + 8y = 24
4x - 8y = -12 (add)
10x = 12 (divide both sides by 10)
x = 1.2 (plug in to either equation, we did 4x - 8y = -12)
4 (1.2) - 8y = -12
4.8 -8y = -12 (subtract 4.8 from both sides)
-8y = 16.8 (divide both sides by 8)
y = 2.1
x2 + 7x - 18
Solve for x
x=2,−9
Work: x2 + 7x - 18 = 0 (add 18 to both sides)
x2 + 7x = 18 (factor)
(x + 2) (x - 9)
x =2, -9
Simplify: (5x3y4z5)3
125x9y12z15
Work:
(Distribute the 3 to everything in the parenthesis)
1- 4x </ 21 and 5x + (7^2) >/ 69
Solve.
x >/ -5 and x >/ 4
1- 4x </ 21 (subtract 1)
-4x </ 20 (divide by -4 & flip the sign)
x >/ -5
5x + (7^2) >/ 69 (solve 7^2)
5x + 49 >/ 69 (subtract 49)
5x >/ 20 (divide by 5)
x >/ 4
Solve: -3(4x+3)+4(6x+1)=43
x=4
Work:
-3(4x+3)+4(6x+1)=43 (substitute)
-12x-9+24x+4=43 (combine like terms)
12x-5=43 (add 5)
12x=48 (divide 12)
x=4
5r + 2s = 23
4r + s = 19
Solve with substitution
r = 2
s = -1
Work: To get "s" alone subtract 4r from both sides (4r + s = 19)
Then you get s = -4r + 19 (plug in to 5r + 2s = 23)
5r + 2(-4r + 19) = 23
5r - 8r + 38 = 23 (Combine like terms then subtract 38 from both sides)
-3r= -15
r = 2
What is a polynomial called with 4 terms?
A quadrinomial