Polynomials and Equations

Equation is a statement that say 2 expressions are equal. Ex: 3x+3=2x-1

Solution or root of an equation is the value of the variable that makes an equation true.

Simple Equations

To solve one step equation, do opposite operation to isolate the variable. Ex: x+4=13
x +4 -4 = 13 -4
x=9

To solve a 2 step equation, either add or subtract to isolate the variable term. Then divide by the coefficient of the variable term. Ex: 2x -7 = 9
2x -7 +7 = 9 +7
2x = 16
2x/2 = 16/2
x=8
Keep in mind that you are using SAMDEB

You can also do a check: L.S. = 2(8) - 7 R.S. = 9
=16 - 7
= 9
L.S. = R.S.

Multi-Step Equations

To solve an equation with Multiple Terms, collect variable terms one side and constant* terms on the other by doing opposite operation. Ex: 3x +2 = 2x -4
3x +2 -2x = 2x -4 -2x
x +2 = -4
x +2 -2 = -4 -2
x = -6

To solve equations with brackets, you need to expand them. 5 (y-3) - (y-2) = 19
5 (y-3) - (y-2) = 19
5y - 15 - y +2 = 19
4y - 13 = 19
4y - 13 + 13 = 19
4y = 32
4y/4 = 32/4
y=8

Check: L.S.= 5 (y-3) - (y-2) R.S.= 19
=5y - 15 - y +2
= 5 (8) - 15 - (8) + 2
=40 -15 -6
= 19
L.S.= R.S.

Equations with fractions

Eliminate the fraction by multiplying both side of the equation by the denominator.

6 = ⅓ (8+x)
3 ✕ 6 = 3 ✕ ⅓ (8+x)
18 = 8 + x
18 - 8 = 8 + x - 8
10 = x

For more than one fraction, find the LCD and multiply all the terms on both sides of equation by this value.

k + 2/3 = k - 4/ 5
15 ✕ k + 2/3 = 15 ✕k - 4/ 5
5 (k+2) = 3 (k-4)
5k + 10 = 3k - 12
5k + 10 - 3k - 10 = 3k - 12 - 3k - 10
2k = - 22
2k/2 = - 22/2
k = - 11

Modelling with Formulas

Algebraic relationship between two or more variables.

To rearrange, isolate the term that contains the variable, and then isolate the variable.

1 step: d = a + b
d - b = a + b - b
d - b = a
Or a = d - b

More then 1 step: y = mx + b
y - b = mx + b - b
y - b = mx
y - b/m = mx/m
y - b/m = x
Or x = y - b/m

Modelling with Algebra

It is a representation of a pattern of numbers.

Example: Alexa works at a record shop. She earns $!0.70/hr plus $0.88 for each album she sells. To model this situation we can say, "h " is the number of hours worked and "a" is the number of albums sold. The expression would be 10.70 h + 0.88 a