Welcome back to Make Sense of Expressions and Inequalities! In the previous lessons, you worked with expressions and used them to represent quantities in real situations. Now you are ready for the next step: learning how to tell whether a math statement is an expression, an equation, or an inequality, and what each one means. Specifically, you will be able to:

• Identify whether a mathematical statement is an expression, equation, or inequality by looking for comparison symbols.
• Explain the purpose of each form: an expression describes a quantity, an equation shows an exact value, and an inequality shows a limit or range.
• Match real-world situations to the correct form based on whether the situation describes a quantity, an exact amount, or a boundary.

So far, we have focused entirely on expressions. An expression like $4h + 25$ tells us what to compute — multiply h by 4, then add 25 — but it never makes a claim about the result. It does not say the result equals something or must stay below something. It simply calculates a quantity and stops there.

In real life, though, we often need to go further. You might need to say that a total is exactly $100, or that a budget must not exceed $500. That is where equations and inequalities enter the picture. Let's explore what makes each of the three forms distinct and when we would reach for one over the others.

An expression is a combination of numbers, variables, and operations that represents a value. It contains no comparison symbol of any kind. Here are a few examples:

• $3x + 10$
• $\frac{n}{4} - 7$

An equation is formed when you take an expression and declare that it equals a specific value or another expression. The defining feature is the equals sign ($=$). For example:

This statement says: "The quantity $3x + 10$ is exactly 40." That one small symbol changes everything. Unlike an expression, an equation can be true or false depending on the value of the variable. If , then , and the equation is true. If , it is not.

An inequality looks similar to an equation, but it replaces the equals sign with an inequality symbol. The four common symbols are:

Here is an example using our familiar expression:

Let's put the three forms next to each other using a single scenario. Imagine a food truck sells tacos for $2 each and charges a $5 service fee. If $t$ = the number of tacos ordered, then the pricing formula is $2t + 5$.

Choosing the wrong form can lead to real confusion. Suppose a friend says, "I only have $25 to spend on tacos," and writes:

This equation says the total is $25, not that it must stay at or below $25. If the friend actually wants to keep spending within a budget, the correct statement is $2t + 5 \leq 25$. The difference is small on paper but large in meaning: an equation locks in one exact outcome, while an inequality opens up a whole range of acceptable outcomes.

In this lesson, you learned to distinguish expressions, equations, and inequalities by looking at their symbols and, more importantly, by understanding their purpose. An expression names a quantity, an equation pins that quantity to an exact value, and an inequality sets a boundary around it. Recognizing which form fits a given situation is a skill we will rely on throughout the rest of this course and beyond.

Up next, you will put these ideas into practice with a series of hands-on tasks. You will classify algebraic statements, sort them into categories, complete explanations in your own words, and even correct a friend's reasoning error. These exercises are designed to move you from quick recognition to confident understanding, so let's dive in!