When I first started learning algebra in 7th grade, I found the difference between equations and inequalities really confusing. Let me explain how they are different in a way that helped me understand better.

1. What They Are

• Equations: These are statements that say two things are equal. For example, in the equation $2x + 3 = 7$, it shows that if you find the right number for $x$, it will make both sides equal.

• Inequalities: These show a relationship where two things are not equal. For example, $2x + 3 < 7$ means $2x + 3$ is less than 7. This gives us many possible answers for $x$.

2. Types of Solutions

• In equations, you usually get one answer. If you solve $x + 5 = 10$, you find that $x = 5$. That's the only answer!

• With inequalities, you don’t just get one answer. For example, if you solve $x + 5 < 10$, you find $x < 5$. This means $x$ can be any number less than 5, opening up lots of possibilities.

3. How They Look on a Graph

• Equations are shown as a single point or line on a graph. For instance, $y = 2x + 1$ is a straight line.

• Inequalities are shown as shaded areas on a graph. If we graph $y < 2x + 1$, we shade everything below that line. This represents all the values that work for that inequality.

4. The Symbols

• Equations use the equals sign $=$.
• Inequalities use symbols like $<$ (less than), $>$ (greater than), $\leq$ (less than or equal to), and $\geq$ (greater than or equal to) to show the relationships.

In the end, learning about inequalities made my understanding of algebra deeper. It made math feel more interesting!