Chapter 3: Evaluating Expressions

3.1 The "Plug and Chug" Method

Until now, we have been working with letters as placeholders. **Evaluation** is the process of replacing those letters with specific numbers to find a final value. In modern terms, we often call this "plugging in" the values.

The Rule: When you replace a variable with a number, always perform the operations (multiplication, addition, etc.) as written. If a number and a letter are touching (like 5x), remember that they are being multiplied.

3.2 Step-by-Step Evaluation

Let's evaluate the expression 4x + 7 if x = 3.

Identify: Everywhere you see an x, replace it with 3.
Substitute: 4(3) + 7
Calculate: 12 + 7 = 19

Important: Use parentheses when substituting. It prevents mistakes, especially when dealing with multiplication or negative numbers.

3.3 Real-World Applications

Scenario 1: Delivery Apps

A delivery fee is calculated using the expression 5 + 0.50m, where m is the number of miles from the restaurant. If you live 8 miles away, what is the fee?

Evaluation: 5 + 0.50(8)
Step 1: 5 + 4
Result: $9.00

Scenario 2: Energy Usage

Your electricity bill is 20 + 0.12k, where k is the kilowatt-hours used. If you used 500 kWh this month, what is your total?

Evaluation: 20 + 0.12(500)
Step 1: 20 + 60
Result: $80.00

3.4 Evaluating with Multiple Variables

Sometimes you will have more than one variable to replace. For example, find the value of 3a + 2b if a = 4 and b = 5.

Plug in for a: 3(4) + 2b
Plug in for b: 3(4) + 2(5)
Multiply: 12 + 10
Final Answer: 22

Quick Check

Try these on your own before moving to Chapter 4:

Evaluate 10x - 4 when x = 5.
Evaluate ab + c when a = 2, b = 3, and c = 10.
A car's rental cost is 40d + 0.25m. If you rent it for d = 2 days and drive m = 100 miles, what is the cost?

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Doctor's Recommendation: Substitution Without the Mess

In this chapter, we practiced "plugging in" numbers for letters. This requires careful substitution, and even a small slip-up can change the entire result. To keep your work clean, the Doctor suggests a tool that allows for infinite "do-overs."

Pilot FriXion Erasable Gel Pens are a favorite for math students. Unlike messy pencils that smudge or standard pens that require "scribbling out" mistakes, these allow you to erase your variable and write the number in its place just as clearly as a fresh page. It makes the multi-step evaluation process much less frustrating.

View Erasable Pens on Amazon

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Doctor's Recommendation: The Equation Scratchpad

Solving your first equations in Chapter 4 is all about finding a rhythm. It often involves a bit of trial and error as you learn to "undo" operations to isolate the variable. To save your paper (and your sanity), the Doctor recommends a dedicated workspace.

A Dry Erase Lapboard with Grid is the perfect companion for this stage. The grid lines help you keep your equal signs stacked vertically—a crucial habit for organized algebra—while the dry-erase surface lets you quickly wipe away a mistake and try again without the frustration of eraser shavings.

View Dry Erase Lapboards on Amazon

Reference: image_80c323.png