Solve a one-step equation with a variable.

SECTION 1

Historical Context & Motivation

Long ago, people needed to solve problems like sharing land or trading goods. They used simple math rules that led to equations. An equation is like a balanced scale. Today, we use a letter like x for the unknown number.

2000 BC

Ancient Egyptians solved simple equations for pyramid building and farming shares.

1800 BC

Babylonian Math

Babylonians wrote equations on clay tablets for business and land.

820 AD

Birth of Algebra

Al-Khwarizmi wrote the first algebra book, giving us the word 'algebra'.

Today

Equations help in video games, sports stats, and SSAT tests!

These ideas fixed real problems. Now, you can solve one-step equations quickly. Let's learn how!

SECTION 2

Core Principles & Definitions

An equation shows two sides that are equal, like 3 + 2 = 5. A one-step equation has a variable (like x) and needs one math move to solve. The key rule is balance: do the same to both sides.

Addition Equations

Like x + 4 = 9. Subtract 4 from both sides.

Subtraction Equations

Like x − 2 = 7. Add 2 to both sides.

Multiplication Equations

Like 5x = 20. Divide both sides by 5.

Division Equations

Like x / 3 = 6. Multiply both sides by 3.

⚖️ Seesaw Analogy

Think of an equation like a seesaw in the park. If one side goes down, the other must too unless you add or remove the same weight from both. Balance wins!

SECTION 3

Visual Explanation with Balance Scale

The left pan has x and 3 units. The right has 7. Subtract 3 from both to balance and find x = 4.

See how the scale tips back to even? That's what solving does. You isolate the variable (get x alone) with one step. Great job picturing it!

SECTION 4

Mathematical Framework

Use the inverse operation. Addition's inverse is subtraction. Do it to both sides to keep balance.

ADDITION

𝑥 + 𝑎 = 𝑏

Subtract a: 𝑥 = 𝑏 − 𝑎 (a is a number)

SUBTRACTION

𝑥 − 𝑎 = 𝑏

Add a: 𝑥 = 𝑏 + 𝑎

MULTIPLICATION

𝑎 × 𝑥 = 𝑏

Divide by a: 𝑥 = 𝑏 ÷ 𝑎

DIVISION

𝑥 ÷ 𝑎 = 𝑏

Multiply by a: 𝑥 = 𝑏 × 𝑎

SECTION 5

Detailed Breakdown by Type

Each box shows a type, the inverse step, and the answer. Follow the pattern!

Match the operation with its inverse. Practice these, and you'll ace SSAT questions. You're getting stronger!

SECTION 6

Step-by-Step Worked Example

Solve 4x = 20

Step 1: Identify the operationx is multiplied by 4. Use inverse: divide by 4.

Step 2: Divide both sides4x ÷ 4 = 20 ÷ 4

x = 5

Step 3: Check4 × 5 = 20. Yes!

Always check your answer. It builds confidence for the test!

SECTION 7

Strengths, Limitations & Common Errors

Avoid these traps to score high!

Mistake	Why Wrong	Correct Way
Only change one side	Breaks balance, like pushing one side of a seesaw	Do same to both sides
Wrong inverse (add for ×)	Doesn't isolate x	Use ÷ for ×, + for −
Forget to check	Misses errors	Plug back in always

✦ KEY TAKEAWAY

One-step equations are quick and build skills for harder math, like game levels unlocking the next.

SECTION 8

Connection to Advanced Equations

One-Step	Two-Step (Next Level)
x + 3 = 7 → x = 4	2x + 3 = 7 → x = 2
One operation	Two operations, same rules

Master one-step now. It prepares you for multi-step on SSAT and beyond. You've got this!

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

What does solving x + 4 = 9 do? A) Finds x = 13 B) Isolates x by subtracting 4 C) Adds 4 to 9 D) Multiplies both sides E) x = 5

PROBLEM 2 — BASIC CALCULATION

Solve x − 2 = 6. A) 4 B) 8 C) x = 8 D) x = 4 E) 3

PROBLEM 3 — INTERMEDIATE

Solve 3x = 12. A) x = 4 B) x = 36 C) x = 9 D) x = 4 E) x = 3

PROBLEM 4 — APPLIED

Sam has 5 times as many cards as x, totaling 25. Solve 5x = 25. A) 3 B) 5 C) x = 5 D) 20 E) 30

PROBLEM 5 — CRITICAL THINKING

Solve x / 4 = 7/2. (Hint: 7/2 = 3.5) A) x = 11/2 B) x = 14 C) x = 3 D) x = 14 E) x = 28/2

SUMMARY

Lesson Summary

You can now solve one-step equations by using inverse operations on both sides. Remember the balance scale like a seesaw!

Practice keeps you sharp for SSAT. You're ready—great work!