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.