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Learn how to find a mystery number hiding behind a letter in one simple step!
People have been solving puzzles with missing numbers for thousands of years! Long before anyone used letters like x or n, people wrote out word puzzles to find unknown amounts.
An equation (ee-KWAY-zhun) is just a math sentence that says two things are equal. Think of it like a balanced seesaw!
So here's the big question: if someone tells you that a mystery number plus 3 equals 10, how do you figure out the mystery number? That's exactly what this lesson will teach you!
Before we start solving, let's learn the key ideas. These are like the rules of the game!
Let's look at a picture that shows how equations work. Imagine a balance scale, like the ones you might see in a science class. Each side must weigh the same!
See how both sides stay even? That's the most important rule. When we subtracted 3 from the left side, we also subtracted 3 from the right side. The letter n ended up all alone, and we found our answer: n = 4!
To solve a one-step equation, you use the inverse operation (in-VERS op-er-AY-shun). That's just a fancy way of saying "the opposite." Here are the four types you'll see on the ISEE.
The secret to solving one-step equations is knowing which operation undoes which. Let's see all four pairs side by side, then look at a picture that puts it all together.
| You See This | Do This | Example |
|---|---|---|
| n + a number | Subtract that number | n + 6 = 10 → n = 10 − 6 = 4 |
| n − a number | Add that number | n − 4 = 9 → n = 9 + 4 = 13 |
| a number × n | Divide by that number | 5 × n = 20 → n = 20 ÷ 5 = 4 |
| n ÷ a number | Multiply by that number | n ÷ 3 = 6 → n = 6 × 3 = 18 |
Let's solve a problem together, just like you'd see on the ISEE. Take it one step at a time!
The ISEE loves to test whether you pick the right operation. Here are some strategies and traps to watch out for!
| Strategy | Why It Helps |
|---|---|
| Use the opposite operation | This is the #1 tool. Addition undoes subtraction. Multiplication undoes division. It works every time! |
| Check by plugging back in | Put your answer in place of the letter. If both sides are equal, you're correct. |
| Try the answer choices | If you're stuck, try each answer choice in the equation. One of them will make both sides equal! |
| Never leave a blank | There's no penalty for wrong answers on the ISEE. Always guess if you're not sure! |
| Watch for tricky wording | "How many more" means subtraction. "Times as many" means multiplication. Read carefully! |
Once you master one-step equations, you'll be ready for bigger challenges! Here's a peek at how one-step equations compare to the next level.
| Feature | One-Step Equation | Two-Step Equation |
|---|---|---|
| How many moves? | Just 1 | 2 moves |
| Example | n + 5 = 12 | 2 × n + 5 = 13 |
| Difficulty | Great starting point! | A bit harder, but same idea |
| On the ISEE Lower Level? | Yes — very common! | Sometimes, as harder questions |
The great news is that two-step equations use the exact same skills you're learning now. You just do the opposite operation twice instead of once. Master one-step equations first, and you'll be ready!
Time to test your skills! Try each problem on your own first. Remember: find the operation, use the opposite, and check your answer. You've got this!
An equation is a math sentence with an equals sign. A one-step equation needs just one move to solve. To find the unknown (the mystery number), use the inverse (opposite) operation on both sides. Addition undoes subtraction. Multiplication undoes division.
Follow the 3-step strategy: (1) spot the operation, (2) do the opposite to both sides, and (3) check your answer by plugging it back in. On the ISEE, if you're stuck, try each answer choice in the equation — one will work! And remember, there's no penalty for guessing, so always answer every question. You've got this!