What Does It Mean to Evaluate an Expression?
Evaluating an expression means replacing a variable, like [latex] x [/latex] or [latex] y [/latex], with a given number and then calculating the result.
Simple Example
Let’s start with a simple example. If you need to evaluate [latex] 2x + 4 [/latex] when [latex] x = 6 [/latex], here’s what you do. You replace the variable [latex] x [/latex] with 6. So, it becomes [latex] 2 times 6 + 4 [/latex]. When you calculate that, [latex] 2 times 6 [/latex] is 12, and then you add 4 to get 16. So, the final result is 16.
The GED test will have more complex problems, but the basic principle remains the same. Let’s look at a couple more examples to make this clear.
Example 1: Multiple Variables
Imagine you need to find the value of [latex] 2x + 5y – 4 [/latex] when [latex] x = 2 [/latex] and [latex] y = -3 [/latex]. First, you replace [latex] x [/latex] with 2 and [latex] y [/latex] with -3. This gives you [latex] 2 times 2 + 5 times (-3) – 4 [/latex]. Now, calculate it step-by-step. [latex] 2 times 2 [/latex] is 4. Then, [latex] 5 times (-3) [/latex] is -15. So, you have [latex] 4 – 15 – 4 [/latex]. When you simplify that, you get -15. So, the final result is -15.
Example 2: Using Exponents
Let’s evaluate [latex] 5x^2 + 2y [/latex] when [latex] x = 2 [/latex] and [latex] y = -3 [/latex]. First, substitute [latex] x [/latex] with 2 and [latex] y [/latex] with -3. This gives you [latex] 5 times 2^2 + 2 times (-3) [/latex]. Calculate it step-by-step. [latex] 2^2 [/latex] is 4, so [latex] 5 times 4 [/latex] is 20. Then, [latex] 2 times (-3) [/latex] is -6. So, you have [latex] 20 – 6 [/latex], which equals 14. So, the final result is 14.
Practice Problem
Let’s solve one more problem. Evaluate [latex] 3x – 4y + 7 [/latex] when [latex] x = 1 [/latex] and [latex] y = 2 [/latex]. Replace [latex] x [/latex] with 1 and [latex] y [/latex] with 2. So, it becomes [latex] 3 times 1 – 4 times 2 + 7 [/latex]. When you calculate it, [latex] 3 times 1 [/latex] is 3, then [latex] 4 times 2 [/latex] is 8. Now we have [latex] 3 – 8 + 7 [/latex] which equals 2.
Additional Example
Here’s another example. If 50+20x is the expression that shows how much money Carlos has saved to buy his new bicycle, where 50 is the amount he has already saved and
x is the number of weeks he continues to save, how much will he save after 8 weeks?
To solve it, we need to replace [latex] x [/latex] with 8. Now the expression is [latex] 50 + 20 times 8 [/latex]. Let’s do the math step-by-step: [latex] 20 times 8 [/latex] is 160. Then, we add 50 to 160. So Carlos will have saved 210 dollars after 8 weeks.
Conclusion
As you can see, evaluating expressions is not complicated, and you can quickly solve these math problems. Knowing how to do this will help you solve other math questions related to evaluating functions that you will learn later on. Let’s solve a few quizzes to practice!
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