Algebra Class Basics

Distributive Property

• The equation 5(7+3)5(7 + 3)5(7+3) demonstrates the distributive property of multiplication over addition.
• The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

Order of Operations

• To simplify the expression 12−4+312 - 4 + 312−4+3, we follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
• Therefore, we first perform the subtraction: 12−4=812 - 4 = 812−4=8, and then the addition: 8+3=118 + 3 = 118+3=11.

Evaluating Expressions

• Given x=3x = 3x=3 and y=4y = 4y=4, we substitute these values into the expression 2x+3y2x + 3y2x+3y.
• This gives: 2(3)+3(4)=6+12=182(3) + 3(4) = 6 + 12 = 182(3)+3(4)=6+12=18.

Inverse Operation

• The inverse operation for addition is subtraction.
• Subtraction "undoes" addition, meaning that adding a number and then subtracting the same number results in the original number.

Interpreting Expressions

• The expression 3(x+4)3(x + 4)3(x+4) represents multiplying the quantity (x+4)(x + 4)(x+4) by 3.
• This means that we distribute the multiplication to both terms inside the parentheses: 3(x+4)=3x+123(x + 4) = 3x + 123(x+4)=3x+12.

The Distributive Property

• The equation $5(7 + 3)$ demonstrates the distributive property of multiplication over addition. This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.

Order of Operations

• To simplify $12 - 4 + 3$, follow the order of operations, which is often remembered by PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):
  • $12 - 4 + 3 = 8 + 3 = 11$

Evaluating Expressions

• If $x = 3$ and $y = 4$, substitute these values into the expression $2x + 3y$ and evaluate:
  • $2(3) + 3(4) = 6 + 12 = 18$

Inverse Operations

• The equation representing the inverse operation for addition is subtraction:
  • $a + b = c$ is equivalent to $c - b = a$

Simplifying Expressions

• The expression $3(x + 4)$ is a combination of multiplication and addition. It can be interpreted as:
  • Multiplying the sum of $x$ and $4$ by $3$, or
  • Distributing the $3$ to both terms inside the parentheses: $3x + 12$

Equations

• The equal sign of an equation shows how two expressions are equivalent.
• An equation is a mathematical statement that asserts the equality of two expressions.
• To solve an equation means to isolate the variable on one side by performing inverse operations on both sides.

Mathematical Terms

• In mathematics, a constant is any numeral or symbol that represents a value.
• The inverse of addition is subtraction, meaning they undo each other.