Algebra I Full Course: Lesson 1

1

Lesson 1: Transition from arithmetic to algebra

1.1

Lesson 1: Transition from arithmetic to algebra

Constants:

1.2

Lesson 1: Transition from arithmetic to algebra

Constants: Coefficients:

1.3

Lesson 1: Transition from arithmetic to algebra

Constants: Coefficients: Variables: 1.4

2

Constants: are values that do not change within a given mathematical problem or expression. They are fixed numbers or symbols that represent a specific value. For example, in the equation y = 3x + 5, the number 5 is a constant because it remains the same throughout the problem. Common constants in mathematics include numbers like π (pi) and e, which represent specific mathematical values.

2.1

3

Coefficients: are the numerical factors that multiply variables in a mathematical expression or equation. They are constants that indicate the magnitude or strength of the relationship between variables. In the equation y = 3x + 5, the number 3 is a coefficient, as it multiplies the variable 'x' to determine the value of 'y'. Coefficients can be positive, negative, whole numbers, fractions, or decimals, but they do not change within a given problem or expression.

3.1

4

4.1

5

Some Practical Examples

5.1

Some Practical Examples

3x 5.2

Some Practical Examples

3x 5.3

Some Practical Examples

3x

Variable

5.4

Some Practical Examples

3x

Variable

5.5

Some Practical Examples

3x

Variable

Coefficient

5.6

6

Constants are numbers

6.1

Constants are numbers

e 6.2

Constants are numbers

e

5 2 6.3

Constants are numbers

e

5 2

−7 6.4

π

Constants are numbers

e

5 2

−7 6.5

7

Algebraic Expressions

7.1

Algebraic Expressions A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).

7.2

Algebraic Expressions A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).

Example:

7.3

Algebraic Expressions A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).

Example:

3x − 7

7.4

Algebraic Expressions A combination of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, and division).

Example:

3x − 7

3x2 + 3x + 1

7.5

8

Equations

8.1

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

8.2

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

8.3

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

2x + 9 = 78 8.4

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

2x + 9 = 78 Linear Equation 8.5

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

2x + 9 = 78 Linear Equation 8.6

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

2x + 9 = 78 Linear Equation

Quadratic Equation 8.7

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

2x + 9 = 78 Linear Equation

↙ Quadratic Equation 8.8

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

2x + 9 = 78 Linear Equation

↙

Exponent 2

Quadratic Equation 8.9

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

↘

2x + 9 = 78

Linear Equation

↙

Exponent 2

Quadratic Equation 8.10

Equations A mathematical statement that two expressions are equal. It usually contains an equal sign (=).

Exponent 1

↘

2x + 9 = 78

Linear Equation

↙

Exponent 2

Quadratic Equation 8.11

9

Like Terms

9.1

Like Terms "Like terms" refer to terms that have the same variables raised to the same power.

In other words, terms that only differ by their coefficients are considered like terms.

9.2

10

For example, in the expression 3x + 2y - 5x - 7, the terms 3x and -5x are like terms because they both have the variable x raised to the first power.

10.1