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.
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.
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.
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.
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.
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.