Home

Tutoring

Subjects

Live Classes

Study Coach

Essay Review

On-Demand Courses

Colleges

Games

Opening subject page...

Loading your content

  1. SSAT Middle Level Quantitative

  3. Solve a one-step equation with a variable.

SSAT Middle Level • Quantitative

Solve a one-step equation with a variable.

Find the missing number by keeping both sides of the equation balanced, like a perfect seesaw.

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.

1

Addition Equations

Like x + 4 = 9. Subtract 4 from both sides.
2

Subtraction Equations

Like x − 2 = 7. Add 2 to both sides.
3

Multiplication Equations

Like 5x = 20. Divide both sides by 5.
4

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

Solving One-Step Equations with a Balance Scale If both sides are equal, we can subtract the same amount from each side. Step 1: x + 3 = 7 Left Side x + 3 Right Side 7 = Step 2: Subtract 3 from both sides − 3 − 3 Step 3: x = 4 x = 4 4 = Left Side Right Side Balanced!
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

Detailed Breakdown by Type Four types of one-step equations — each solved with the inverse operation Addition x + 5 = 12 subtract 5 −5 from both sides x = 7 Subtraction x − 4 = 9 add 4 +4 to both sides x = 13 Multiplication 3x = 15 divide by 3 ÷3 on both sides x = 5 Division x ÷ 2 = 6 multiply 2 ×2 on both sides x = 12 💡 Tip: Always use the inverse operation to isolate the variable.
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 operation

x is multiplied by 4. Use inverse: divide by 4.

Step 2: Divide both sides

4x ÷ 4 = 20 ÷ 4
x = 5

Step 3: Check

4 × 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!
MistakeWhy WrongCorrect Way
Only change one sideBreaks balance, like pushing one side of a seesawDo same to both sides
Wrong inverse (add for ×)Doesn't isolate xUse ÷ for ×, + for −
Forget to checkMisses errorsPlug 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-StepTwo-Step (Next Level)
x + 3 = 7 → x = 42x + 3 = 7 → x = 2
One operationTwo 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!

Varsity Tutors • SSAT Middle Level • Solve a one-step equation with a variable.