Solving Basic Equations Addition-Subtraction

Introduction to Algebra

  • Algebra involves equations with variables (unknown values).

  • Solving an equation means finding the value of the variable.

  • This video will focus on solving simple algebraic equations using addition and subtraction.

Understanding Equations

  • Key strategy: Rearrange the equation to isolate the unknown on one side.

  • The other side should contain all known values.

  • An equation can be thought of as a balance scale: both sides must be equal.

  • Example: In the equation 1 + 1 = 2, both sides have the same value despite looking different.

  • If the balance is disrupted, the equation will no longer be true.

Keeping Equations in Balance

  • Whenever changes are made to an equation, the same change must occur on both sides.

  • This principle applies to addition, subtraction, multiplication, and division.

    • Adding a number to one side means adding it to the other side as well.

    • Subtracting from one side calls for subtracting from the other side too.

    • The same applies for multiplication and division.

  • Maintaining balance is crucial to ensure that the equation remains true.

Solving Simple Equations with Addition

  • Example: x + 7 = 15

    • To isolate x, subtract 7 from both sides:

      • x + 7 - 7 = 15 - 7

      • Thus, x = 8.

    • Check: Replace x with 8 in the original equation: 8 + 7 = 15 (true).

  • Example: 40 = 25 + x

    • Rearranging gives x = 40 - 25.

    • Solve: x = 15.

Solving Simple Equations with Subtraction

  • Example: x - 5 = 16

    • To isolate x, add 5 to both sides:

      • x - 5 + 5 = 16 + 5

      • Thus, x = 21.

  • Example: 10 = x - 32

    • Rearranging gives x = 10 + 32.

    • Solve: x = 42.

Trickier Subtraction Problems

  • Example: 12 - x = 5

    • Need to isolate x, but subtracting 12 would lead to a negative unknown.

    • Instead, add x to both sides:

      • 12 = 5 + x.

  • Now, isolate x by subtracting 5:

    • x = 12 - 5 = 7.

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