In this guide, we'll walk through Linear Equations — Complete Guide with Examples step by step. Whether you're revising for an exam or practising linear equations, this clear walkthrough will help you understand not just the answer, but the reasoning behind every step.

Quick Answer

See the step-by-step solution above for the complete answer.

Step-by-Step Solution

Step 1: Start with: -5x + -2 = -22

Step 2: Subtract -2 from both sides: -5x = -22 - (-2) = -20

Step 3: Divide both sides by -5: x = -20/-5 = 4

Step 4: Start with: -5x + -2 = -22

Step 5: Subtract -2 from both sides: -5x = -22 - (-2) = -20

Step 6: Divide both sides by -5: x = -20/-5 = 4

Step 7: Start with: -7x + -11 = -10

Step 8: Subtract -11 from both sides: -7x = -10 - (-11) = 1

Step 9: Divide both sides by -7: x = 1/-7

Step 10: Start with: 4x + -16 = -19

Step 11: Subtract -16 from both sides: 4x = -19 - (-16) = -3

Step 12: Divide both sides by 4: x = -3/4

Step 13: Start with: -7x + 24 = 12

Step 14: Subtract 24 from both sides: -7x = 12 - 24 = -12

Step 15: Divide both sides by -7: x = -12/-7

Step 16: Start with: -7x + -8 = 5

Step 17: Subtract -8 from both sides: -7x = 5 - (-8) = 13

Step 18: Divide both sides by -7: x = 13/-7

Step 19: Start with: -5x + 10 = 11

Step 20: Subtract 10 from both sides: -5x = 11 - 10 = 1

Step 21: Divide both sides by -5: x = 1/-5

Step 22: Start with: -4x + 12 = 13

Step 23: Subtract 12 from both sides: -4x = 13 - 12 = 1

Step 24: Divide both sides by -4: x = 1/-4

Step 25: Start with: 9x + -11 = -9

Step 26: Subtract -11 from both sides: 9x = -9 - (-11) = 2

Step 27: Divide both sides by 9: x = 2/9

Step 28: Start with: -3x + -15 = -3

Step 29: Subtract -15 from both sides: -3x = -3 - (-15) = 12

Step 30: Divide both sides by -3: x = 12/-3 = -4

Step 31: Start with: 3x + 0 = 5

Step 32: Subtract 0 from both sides: 3x = 5 - (0) = 5

Step 33: Divide both sides by 3: x = 5/3

Step 34: Start with: 7x + -11 = -4

Step 35: Subtract -11 from both sides: 7x = -4 - (-11) = 7

Step 36: Divide both sides by 7: x = 7/7 = 1

Step 37: Start with: 7x + 16 = 13

Step 38: Subtract 16 from both sides: 7x = 13 - 16 = -3

Step 39: Divide both sides by 7: x = -3/7

Step 40: Start with: -7x + -10 = -17

Step 41: Subtract -10 from both sides: -7x = -17 - (-10) = -7

Step 42: Divide both sides by -7: x = -7/-7 = 1

Step 43: Start with: -4x + -3 = 15

Step 44: Subtract -3 from both sides: -4x = 15 - (-3) = 18

Step 45: Divide both sides by -4: x = 18/-4

Step 46: Start with: -2x + 19 = -19

Step 47: Subtract 19 from both sides: -2x = -19 - 19 = -38

Step 48: Divide both sides by -2: x = -38/-2 = 19

Step 49: Start with: 7x + -6 = -11

Step 50: Subtract -6 from both sides: 7x = -11 - (-6) = -5

Step 51: Divide both sides by 7: x = -5/7

Step 52: Start with: 2x + 20 = 24

Step 53: Subtract 20 from both sides: 2x = 24 - 20 = 4

Step 54: Divide both sides by 2: x = 4/2 = 2

Step 55: Start with: 7x + 20 = 15

Step 56: Subtract 20 from both sides: 7x = 15 - 20 = -5

Step 57: Divide both sides by 7: x = -5/7

Step 58: Start with: -9x + -17 = -25

Step 59: Subtract -17 from both sides: -9x = -25 - (-17) = -8

Step 60: Divide both sides by -9: x = -8/-9

Step 61: Start with: -5x + 2 = -18

Step 62: Subtract 2 from both sides: -5x = -18 - 2 = -20

Step 63: Divide both sides by -5: x = -20/-5 = 4

Why This Works

This problem uses linear equations. The key idea is to perform the same operation on both sides to keep the equation balanced. Each step brings you closer to isolating the unknown variable.

Common Mistakes to Avoid

❌ Mistake 1: Forgetting to apply the same operation to both sides of the equation.

❌ Mistake 2: Making sign errors when moving terms across the equals sign.

❌ Mistake 3: Not simplifying the final answer completely.

Practice Similar Problems

• Solve: x² - 12x + 35 = 0
• Solve: x² + 9x - 36 = 0
• Solve: x² + 0x - 49 = 0
• Solve: x² - x - 30 = 0
• Solve: x² + 20x + 96 = 0

Frequently Asked Questions