Fix the mistake: Linear Equations

Linear Equations ① How to Solve Equations

In this lesson, you will learn the basic methods for solving linear equations. You will use the “properties of equality” to find the value of the unknown x.

Properties of Equality

  • An equation remains true when the same number is added to both sides
  • An equation remains true when the same number is subtracted from both sides
  • An equation remains true when both sides are divided by the same number (division by 0 is not allowed)
  • An equation remains true when both sides are multiplied by the same number
Example 1 (Basic)
Solve 3x＋5＝14.

Solution:
3x＝14－5
3x＝9
x＝3

Rules for Transposing Terms

Moving a term from one side of an equation to the other while changing its sign is called transposing a term.

Example 2 (When x appears on both sides)
Solve 5x－3＝2x＋9.

Solution:
5x－2x＝9＋3
3x＝12
x＝4
Example 3 (When parentheses are present)
Solve 3(x＋2)＝2(x－1)＋11.

Solution:
3x＋6＝2x－2＋11
3x－2x＝－2＋11－6
x＝3
Key Points
  • When transposing a term, its sign changes（＋↔−）
  • Collect the terms containing x on the left side and the numbers on the right side
  • Expand the parentheses first

Practice Problems

  1. Solve 4x－7＝13.
  2. Solve 2(3x－1)＝4x＋8.

Answers and Explanations

  1. Answer:x＝5
    Explanation: 4x＝13＋7＝20. x＝20÷4＝5. Check: 4×5－7＝13 ✓
  2. Answer:x＝5
    Explanation: Expand the parentheses: 6x－2＝4x＋8. Transpose the terms: 6x－4x＝8＋2. 2x＝10. x＝5. Check: 2(3×5-1)＝28＝4×5＋8 ✓

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