A balanced scale with equation symbols on each pan, representing both sides of an equation staying equal.
Unit 4 · Expressions & Equations · 6.EE

Lesson 4.3 — Solving One-Step Equations

An equation is a balanced scale — whatever you do to one side, you must do to the other to find the mystery number.

🎙️ Narration script

Hi again! Today we're solving one-step equations. And here's the picture I want in your head the whole time: a balanced scale.

So what's an equation? It's a math sentence that says two things are equal. It has an equals sign, like x plus three equals seven. When we solve it, we're hunting for the value of the variable that makes the sentence true. A one-step equation only needs one move to get the variable all by itself.

Here's the big trick. To get the variable alone, you do the opposite operation, the inverse, to both sides. Plus undoes minus. Times undoes divide. And whatever you do to one side, you must do to the other, so the scale stays balanced.

Let's solve x plus three equals seven. First, spot what's happening to x: three is being added. So the inverse is to subtract three. But here's the key, subtract three from both sides. On the left, x plus three minus three leaves just x. On the right, seven minus three is four. So x equals four.

And always check your answer. Plug it back in: four plus three equals seven. True! It works.

Let's do one more. Three tickets cost twenty-four dollars total, so three t equals twenty-four. The variable is being multiplied by three, so we do the opposite, divide both sides by three. Twenty-four divided by three is eight. Each ticket is eight dollars.

Quick reminder of the difference: an expression like x plus three has no equals sign, you evaluate it. An equation has an equals sign, you solve it.

So, recap. Keep the scale balanced, do the inverse operation to both sides, isolate the variable, and check by substituting back. You've got this!

1 Core idea

An equation says two things are equal — it has an = sign, like x + 3 = 7. To solve it means finding the value of the variable that makes the sentence true. A one-step equation needs just one move to get the variable alone. The trick: do the opposite (inverse) operation to both sides so the scale stays balanced.

🧩 Think of it like… a balance scale: the = sign is the pivot, and both pans weigh exactly the same. To uncover the mystery weight you remove the same amount from both pans at once, keeping it perfectly level — that is what "do the same thing to both sides" really means.
Where it breaks: a real scale can't hold a negative weight, and you can't literally "divide a pan by 3" — so the picture is flawless for + and −, but you have to stretch your imagination for × and ÷.

2 Key terms

Equation
A math sentence with an equals sign: two sides that are equal.
Solve
Find the value of the variable that makes the equation true.
Solution
The number that, when substituted, makes both sides equal.
Inverse operation
The opposite move: + undoes −, × undoes ÷.
Isolate the variable
Get the letter alone on one side, all by itself.

3 Real-life examples

  • Allowance: You had some money, got $3 more, now have $7. x + 3 = 7 → you had $4.
  • Snacks: You shared cookies equally among 4 friends, each got 5. c ÷ 4 = 5 → you had 20.
  • Saving up: You spent $6 and have $10 left. m − 6 = 10 → you started with $16.
  • Tickets: 3 tickets cost $24 total. 3t = 24 → each ticket is $8.
🤔 Pause & think: To solve x + 3 = 7 we subtract 3. Why subtract it from both sides, instead of just the left side where the "+ 3" actually sits?
Reveal the thinking
The = sign is a promise that the two sides are equal. If you take 3 off only the left, you'd write x = 7 — but that's false, since x is really 4. Removing 3 from both sides keeps the promise true: x + 3 − 3 = 7 − 3, so x = 4. Touch only one pan and the scale tips; touch both equally and it stays balanced.

4 Common doubts

What's the difference between an expression and an equation?

An expression (like x + 3) has no equals sign — you evaluate it. An equation (x + 3 = 7) has one — you solve it.

Why do I do the same thing to both sides?

An equation is like a balanced scale. If you take 3 off one pan, you must take 3 off the other or it tips over.

Which operation do I use?

The opposite of what's done to the variable. If 3 is added, subtract 3. If the variable is multiplied by 3, divide by 3.

How do I know my answer is right?

Plug it back in. For x + 3 = 7 with x = 4: 4 + 3 = 7. True! It checks.

5 Step-by-step (solve x + 3 = 7)

  1. Spot what's done to the variable: 3 is added to x.
  2. Use the inverse: subtract 3 — from both sides.
  3. Simplify: x + 3 − 3 = 7 − 3 becomes x = 4.
  4. Check: substitute back — 4 + 3 = 7. ✓ True.

📊 See it · keep the scale balanced

x+3 7 x + 3 = 7 subtract 3 from both sides x 4 x = 4

Take 3 off both pans and the scale stays level — so x must equal 4.

Solve x + 3 = 7:

x + 3 − 3 = 7 − 3 → subtract 3 from both sides
x = 4 → simplify
Check: 4 + 3 = 7 ✓ → substitute back
✅ Check yourself
  1. Solve 6x = 18.
    answer x is multiplied by 6, so divide both sides by 6: 18 ÷ 6 = 3. Check: 6 × 3 = 18 ✓.
  2. Solve y − 5 = 8.
    answer 5 is subtracted, so add 5 to both sides: 8 + 5 = 13. Check: 13 − 5 = 8 ✓.
⚡ Quick recap. An equation has an = sign and a mystery number to find. Keep it balanced: do the inverse operation to both sides to isolate the variable, then check by substituting your answer back in.

Grounded in CA CCSS-M, Grade 6 · 6.EE.7 (solving one-step equations), California Department of Education. Hero image generated with Gemini Nano Banana Pro.