Evaluate The Expression Single Variable Answer Key

Evaluating Single-Variable Expressions: A Comprehensive Guide with Answer Key

Evaluating expressions, especially those with a single variable, is a fundamental skill in algebra. This guide provides a step-by-step approach to evaluating such expressions, along with example problems and an answer key to help you solidify your understanding. Mastering this skill is crucial for progressing to more complex algebraic concepts.

What is a Single-Variable Expression?

A single-variable expression is a mathematical phrase that contains only one variable (usually represented by letters like x, y, or z), numbers, and mathematical operations (+, -, ×, ÷). For example, 3x + 5, 2y - 7, and x²/4 are all single-variable expressions. The variable acts as a placeholder for a specific numerical value. Evaluating the expression means substituting a given value for the variable and then simplifying the resulting numerical expression to find the final answer.

Step-by-Step Guide to Evaluating Single-Variable Expressions:

1. Substitute: Replace the variable in the expression with the given numerical value. Make sure to enclose the substituted value in parentheses, especially if it's negative or involves fractions, to avoid errors in calculations.

2. Simplify: Follow the order of operations (PEMDAS/BODMAS) to simplify the resulting numerical expression. Remember the acronym:

   • Parentheses (Brackets)
   • Exponents (Orders)
   • Multiplication and Division (from left to right)
   • Addition and Subtraction (from left to right)

3. Solve: Perform the calculations to obtain the final numerical result. This is the value of the expression when the variable is replaced with the given number.

Example Problems:

Let's evaluate the following expressions for x = 3 and y = -2:

Expression 1: 2x + 7

1. Substitute: 2(3) + 7
2. Simplify: 6 + 7
3. Solve: 13

Expression 2: 5y² - 4

1. Substitute: 5(-2)² - 4
2. Simplify: 5(4) - 4 (Remember to square -2 before multiplying)
3. Solve: 20 - 4 = 16

Expression 3: (x + y) / 2

1. Substitute: (3 + (-2)) / 2
2. Simplify: (1) / 2
3. Solve: 0.5 or 1/2

Expression 4: 4x - 3y + 1

1. Substitute: 4(3) - 3(-2) + 1
2. Simplify: 12 + 6 + 1
3. Solve: 19

Answer Key:

• Expression 1 (x = 3): 13
• Expression 2 (y = -2): 16
• Expression 3 (x = 3, y = -2): 0.5 or 1/2
• Expression 4 (x = 3, y = -2): 19

Practice Problems:

Try evaluating these expressions for the given values:

1. 3x² + 2x - 5 (x = 2)
2. -y³ + 7y - 1 (y = -1)
3. (2a + b) / (a - b) (a = 4, b = 2)
4. 5p - 2q + 8 (p = -3, q = 5)

Remember to follow the steps outlined above and practice consistently to master evaluating single-variable expressions. This foundational skill will pave the way for a stronger understanding of more advanced algebraic concepts. Good luck!