Reteaching 11 Variables & Expressions: Answer Key

When learning algebra, understanding variables and expressions is fundamental. If you've had difficulty grasping these concepts, you're not alone. We're here to reteach and simplify these topics to ensure you grasp them, so let's dive right in.

Variables and expressions are the building blocks of algebra. They allow us to represent numbers we don't know yet and write formulas to solve for them. Let's explore these key concepts and practice with an answer key for better understanding.

Understanding Variables

A variable is a letter (or symbol) used to represent an unknown number in a mathematical equation. In algebra, we often use variables like 'x' and 'y'.

For example, in the equation 5 + 4x - 7 = 10, '4x' is a variable because it represents an unknown number. We can solve for 'x' by following these steps:

Isolating the Variable

To solve for 'x', we first want to get 'x' on one side of the equation by itself. We can do this by adding 7 to both sides and then subtracting 5 from both sides:

• 5 + 4x - 7 = 10
• 4x - 2 = 10 (after adding 7 to both sides)
• 4x = 12 (after adding 2 to both sides)

Now, we have the variable all by itself.

Solving for the Variable

To find the value of 'x', we divide both sides by 4:

• 4x = 12
• x = 3 (after dividing both sides by 4)

So, the solution to the equation 5 + 4x - 7 = 10 is x = 3.

Working with Expressions

An algebraic expression is a combination of variables, numbers, and operations using addition, subtraction, multiplication, and division. To evaluate an expression, we follow the order of operations (PEMDAS/BODMAS).

Let's evaluate the expression 3(2x + 1) - 5. We'll follow PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) order:

Handling Parentheses

First, we solve for the expression inside the parentheses. Since multiplication comes before addition, we calculate 2x inside the parentheses:

• 3(2x + 1) - 5
• 3(2x) + 3(1) - 5 (distributing the 3)

Evaluate Multiplication

Now, we'll multiply 3 by 2x and 3 by 1:

• 6x + 3 - 5
• 6x - 2
(after combining like terms by subtracting 2 from 3)

So, the evaluated expression is 6x - 2.

By understanding variables and expressions and practicing with an answer key, you can build a strong foundation in algebra.If you're eager to grasp more complex concepts, you're on the right track. Keep practicing, and don't hesitate to seek help when needed. Happy learning!