Example Equation:

$3x + 5 = 2x + 8$

Solution:

1. Subtract $2x$ from both sides (Using the Subtraction Property of Equality: if $a = b$, then $a - c = b - c$):
   $3x + 5 - 2x = 2x + 8 - 2x$ $x + 5 = 8$

2. Subtract 5 from both sides (Again, using the Subtraction Property of Equality):
   $x + 5 - 5 = 8 - 5$ $x = 3$

Justification:

• Step 1 is valid because subtracting the same value ($2x$) from both sides preserves equality.
• Step 2 is valid because subtracting the same number ($5$) from both sides maintains balance.

Final Answer:

$x = 3$

Would you like a more detailed breakdown or a different example?

Related Questions:

1. How do you check if your solution to an equation is correct?
2. What happens when solving an equation leads to a contradiction, such as $3 = 5$?
3. Can an equation with variables on both sides have infinitely many solutions?
4. How does the Distributive Property apply when solving equations?
5. What is the importance of the Addition and Multiplication Properties of Equality in solving equations?

Tip:

Always check your solution by substituting it back into the original equation to verify that both sides remain equal!