Simple Linear Equations

Article Contents

1. Introduction to Simple Equations
2. Pattern Recognition
3. The Four Basic Types
4. Step-by-Step Examples
5. Practice Worksheets

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1. Introduction to Simple Equations {#introduction-to-simple-equations}

Simple linear equations have the unknown on only one side and involve basic operations.

The key principle is the balance principle: whatever you do to one side, you must do to the other.

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2. Pattern Recognition {#pattern-recognition}

Learn to recognize these patterns:

Pattern	What to Do
$x+a=b$	Subtract $a$ from both sides
$x-a=b$	Add $a$ to both sides
$ax=b$	Divide both sides by $a$
$x/a=b$	Multiply both sides by $a$

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3. The Four Basic Types {#the-four-basic-types}

Type 1: $x+a=b$

Formula: $x=b-a$

Example: Solve $x+7=15$

$$x=15-7=8$$

Check: $8+7=15✓$

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Type 2: $x-a=b$

Formula: $x=b+a$

Example: Solve $x-5=12$

$$x=12+5=17$$

Check: $17-5=12✓$

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Type 3: $ax=b$

Formula: $x=b/a$

Example: Solve $4x=28$

$$x=28/4=7$$

Check: $4\times 7=28✓$

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Type 4: $x/a=b$

Formula: $x=b\times a$

Example: Solve $x/6=4$

$$x=4\times 6=24$$

Check: $24/6=4✓$

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4. Step-by-Step Examples {#step-by-step-examples}

Example 1

Solve: $x+9=23$

Step 1: Identify the pattern — it's $x+a=b$

Step 2: Subtract 9 from both sides

$$x+9-9=23-9$$

Step 3: Calculate

$$x=14$$

Step 4: Check

$$14+9=23✓$$

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Example 2

Solve: $x-6=11$

Step 1: Identify the pattern — it's $x-a=b$

Step 2: Add 6 to both sides

$$x-6+6=11+6$$

Step 3: Calculate

$$x=17$$

Step 4: Check

$$17-6=11✓$$

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5. Practice Worksheets {#practice-worksheets}

Easy Level

• $x+3=10\Rightarrow x=?$
• $x-4=8\Rightarrow x=?$
• $2x=14\Rightarrow x=?$

Medium Level

• $x+12=25$
• $x-7=15$
• $5x=35$

Answers

• Easy: $7,12,7$
• Medium: $13,22,7$

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Interactive Exercises

• Linear Equations - Basic - Practice simple equations

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