Category:Algebra I

Lesson 1 Combining Like Terms
(Do not combine unlike terms!)

Cart + Cart = 2 Carts

x + x = _________

Lesson 2 Simple Equations
(What you do to the right side of the equation you do to the left side of the equation.)

x + 5 = 12

w - 9 = 15

3x = 36

1/3h = 9

-3/8 = 24

Lesson 3 Solving Equations by using two or more operations
4x - 9 = 23

8x + 14 = 30

1/4x + 6 = 10

1/9x - 5 = 13

2/5x + 3 = 21

Lesson 4 Combining like terms to solve equations
5a + 3a = 40

4x + 2x + x = 27

4e - e + 3e = 120

3x - x + 12 = 24

8y + 4 + y = 85

Lesson 5 Graphing solution sets/number lines
We need to know 4 symbols. < less than > greater than ≤ less than or equal to ≥ greater than or equal to

Less than to the Left

x < 7

x ≥ -4

x > -6

x ≤ 9 1/2

Lesson 6 Review of signed numbers
We will add, subtract, multiply and divide signed numbers. Basically this is a review. It is a two stepped process. First, will it be negative or positive? The sign of the number, with the greatest absolute value will determine this. In the example, 7 + (-5), 7 has the greater absolute value, so the answer will be positive. Second, do we add or subtract? When signs are different, we subtract the absolute values, so 7 - 5 = +2. When the absolute value of the negative number is larger, the answer is a negative number. When both numbers have negative signs, we add the numbers, and the answer is negative.

Add

6 + -4 = +2

-10 + 5 = -5

-5 + -9 = -14

Subtract

8 - 10 = -2 (7 + -9 = -2)

-5 - -7 = +2 (-5 + +7 = +2)

-3 - 1 = -4 (-3 + -1 = -4)

8 - -4 = +12 (8 + +4 = +12)

Multiply

When signs are different, the answer will be negative. If signs are the same, the answer will be positive.

-8 ∙ 3 = -24

+6 ∙ -2 = -12

-5 ∙ -7 = +35

Divide

-21 ∕ -3 = +7

-32 ∕ 8 = -4

20 ∕ -5 = -4

Lesson 7 Evaluating algebraic expressions
We have assigned values to four variables:

a = 1, b = -2, c = 0, x = 1/2

ab - 4b

c + 2a - 6b

3x - 7ac + 8ab

4abx + 5ab

(6a + 7b) ∕ 8ab

Lesson 8 Adding Monomials
This is like Lesson 1. Combine like terms; do not combine unlike terms.

6x + 5x = 11x

-5z + 3z = -2z

6y + -1y = 5y

4yz + 2yz = 6yz (4yz + 2yz = 6yz)

-x + -6x = -7x (-1x + -6x = -7x)

y + y² = y + y² (this is already in its lowest terms)

z + z = 2z (1z + 1z = 2z)

5y² + -y² = 4y² (5y² + -1y² = 4y²)

3xyz + 2xy = 3xyz + 2xy (this is already in its lowest terms)

Lesson 9 Subtracting monomials
Subtract

-7x - +4x =

-3mn - -2mn =

0 - -5x =

-3x² - -6x² =

-8a²b - +6a²b =

Lesson 10 Multiplying monomials
To multiply monomials, we add the exponents.

x² ∙ x³ =

(5yz)(8y³) =

(-4x)(x³y)(y) =

(-3a³b)(-5ab)³(4b²) =

2/5(r²)(rs²t)(7t²s) =

-(1/3)(m)(m³n³)(-4mn²) =

Lesson 11 Dividing monomials
Instead of adding exponents, we will be subtracting exponents.

y³ ∕ y =

-45ab ∕ 9a =

-21xyz ∕ 7xz =

72c³d² ∕ -6c²d =

-64g³h² ∕ 8g²h =

Lesson 12 Adding and subtracting polynomials
Combine like terms, do note combine unlike terms.

Add

(4m + 6n) + (8m - 4n)

Rearange and add. Keep in alphabetical order.

(6x + 2y - z) + (-8y + 3z - 2x) = (6x + 2y - z) + (-2x - 7y + 3z) =

Add

(-7a² + 2b²) - (8a² -3b²)

Subtract

Draw the line, change the sign, and add.

(5ab - 4cd) - (2ab + 7cd) = (5ab - 4cd) + (-2ab - 7cd)

Subtract

(8xy - 4ab) - (6xy - 2cd) = (8xy - 4ab) + (-6xy + 2cd)

Lesson 13 Dividing Polynomials by a bynomial (Polynomials)
4 rules

1. Match the first term by multiplying

2. Draw the line,

3. change the sign,

4. and add

(x² + 7x + 10) ∕ (x + 5)

(3x² + 10x + 3) ∕ (3x + 1)

(x³ + 2x² -5x + 12) ∕ (x + 4)

(18k² - 3kr - 10r²) ∕ (6k - 5r)

(x³ - 3) ∕ (x² + x - 3) = x³ + 0x² + 0x - 3 ∕ x² + x - 3 = x - 1 + (4x - 6) / (x² + x - 3)

Lesson 14 Equations containing parentheses
1. Solve everything inside the parentheses first

2. Remember order of operations

Do multiplication and division first, then do addition and subtraction. Solve for x.

2(x + 3) = 18

5 + 3(x - 2) = 5

2x - (x + 2) = 6

(3x - 1) - (2x + 3) = 6

3x - [x + (4x + 1) + 3] = 6

Lesson 15 Absolute value equations

 * x| = 4


 * x + 1| = 3

+ |x + 2| = -2


 * x + 3| + 1 = 8

2|x + 1| = 6

Lesson 16 Solving equations containing more than one variable
7x/7 = b/7

ry = 3 (Solve for y)

9 + y = c

5 - x = h

a = by + 6

rsx - rs² = 0

Lesson 17 Inequalities containing one variable
If the variables have negative coefficients, such as -5x, the equation is solved by dividing by a negative number, such as -5.

2a - 2 < 8

-5z < 25

-7x > -21

3b + 15 > 9

-2n + 6 > -4

-3s + 6 > s - 30