Evaluate variable expressions with whole numbers
In algebra, letters (like x) stand in for numbers. 'Evaluating an expression' means you get to be the code-breaker! You are given the secret value of the letter, and your job is to plug it in and solve the problem.
Concept
A variable expression is a math phrase that contains numbers, operations (+, -, x, ÷), and at least one variable (a letter, like x or y). To evaluate it, you replace the variable with its given value and then perform the operations. **The Three-Step Process:** 1. **Substitute:** Replace the variable with the number it stands for. It's a good idea to use parentheses when you substitute to keep things clear. 2. **Simplify:** Perform the calculations using the order of operations (PEMDAS). 3. **Solve:** Find the final value of the expression. **Example 1: Evaluate 5x - 3 when x = 4.** 1. **Substitute:** Replace 'x' with 4. * 5(4) - 3 2. **Simplify:** Remember that 5x means 5 *times* x. * 5 x 4 = 20 * Now the expression is 20 - 3. 3. **Solve:** * 20 - 3 = 17. **Example 2: Evaluate y/3 + 2 when y = 12.** 1. **Substitute:** Replace 'y' with 12. * 12/3 + 2 2. **Simplify:** Division comes before addition (PEMDAS). * 12 ÷ 3 = 4 * Now the expression is 4 + 2. 3. **Solve:** * 4 + 2 = 6. **Example with Multiple Variables: Evaluate 2a + 3b when a = 5 and b = 6.** 1. **Substitute:** Replace 'a' with 5 and 'b' with 6. * 2(5) + 3(6) 2. **Simplify:** Do both multiplications. * 2 x 5 = 10 * 3 x 6 = 18 * Now the expression is 10 + 18. 3. **Solve:** * 10 + 18 = 28. **Key Idea:** The variable is just a placeholder. Once you know its value, the problem becomes a regular numerical expression.
Try it
Practice: Evaluate variable expressions with whole numbers.