Solving for an unknown letter in an equation involves isolating this letter on one side of the equation.
Main Rule: Whatever operation you perform on one side of the equation, you must perform on the other side to maintain equality.
Addition and Subtraction
Example 1: Solve (x + 3 = 10)
Objective: Isolate (x).
Steps:
Subtract 3 from both sides to get (x = 7).
Explanation: (3) is being added to (x), so subtract it to cancel out.
After subtraction: (x = 10 - 3 = 7).
Result: (x = 7).
Example 2: Solve (14 = a - 5)
Objective: Isolate (a).
Steps:
Add 5 to both sides to get (a = 19).
Explanation: (-5) is subtracted from (a), so add 5 to cancel it out.
After addition: (a = 14 + 5 = 19).
Result: (a = 19).
Multiplication and Division
Example 3: Solve (3x = 12)
Objective: Isolate (x).
Steps:
Divide both sides by 3 to get (x = 4).
Explanation: (x) is multiplied by 3, so divide by 3 to cancel.
After division: (x = 12 / 3 = 4).
Result: (x = 4).
Example 4: Solve (15 = p / 4)
Objective: Isolate (p).
Steps:
Multiply both sides by 4 to get (p = 60).
Explanation: (p) is divided by 4, so multiply by 4 to cancel.
After multiplication: (p = 15 \times 4 = 60).
Result: (p = 60).
Additional Examples
Example 5: Solve (4 + b = 19)
Objective: Isolate (b).
Steps:
Subtract 4 from both sides to get (b = 15).
Explanation: (4) can be thought of as (+4), so subtract it to isolate (b).
After subtraction: (b = 19 - 4 = 15).
Result: (b = 15).
Example 6: Solve (7x = 28)
Objective: Isolate (x).
Steps:
Divide both sides by 7 to get (x = 4).
Explanation: (x) is multiplied by 7, so divide by 7 to cancel.
After division: (x = 28 / 7 = 4).
Result: (x = 4).
Conclusion
Solving algebraic equations involves isolating the unknown variable by performing inverse operations while maintaining equality on both sides of the equation.
Practice ensures understanding and ease with more complex equations.