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When working with equations, it's crucial to remember the order of operations. This is a standard process that helps everyone understand mathematics the same way. The order of operations tells us the steps to follow when solving any math problem and is often remembered by the acronym PEMDAS.

• Parentheses
• Exponents
• Multiplication & Division (from left to right)
• Addition & Subtraction (from left to right)

But here's a twist! When you're solving equations, you'll actually perform these steps in the reverse order of PEMDAS. This might sound confusing, but think of it this way: when you solve equations, you need to "undo" operations to find the value of the unknown variable. By doing this in reverse, you isolate the variable correctly.

The addition property in algebra is like a trusty tool in your math toolkit. It says if you add the same number to both sides of an equation, the equation still holds true. This property helps keep the equation balanced.
To demonstrate, if you have a simple equation like \( x + 3 = 7 \), you can subtract 3 from both sides to keep it balanced. So you'll have \( x + 3 - 3 = 7 - 3 \), which simplifies to \( x = 4 \).
In the original equation \( 2x + 5 = 17 \), the addition property was used when we performed the reverse operation: subtracting 5 from both sides to help isolate the term with the variable, leading to \( 2x = 12 \). By using the addition property in this way, we're one step closer to finding the solution for \( x \).

The multiplication property of equations is another handy tool. It ensures that multiplying or dividing both sides of an equation by the same non-zero number keeps the equation balanced.
Imagine you have the equation \( x/2 = 3 \). To solve this, you would multiply both sides by 2 to isolate and solve for \( x \). It becomes \( x = 6 \). This property is all about maintaining balance while removing coefficients or fractions in front of a variable.
In the example equation \( 2x + 5 = 17 \), after using the addition property to simplify it to \( 2x = 12 \), we used the multiplication property by dividing both sides by 2. This operation provided the solution \( x = 6 \), giving us the final answer. The key is remembering that multiplication (and division) operations should be executed after handling addition and subtraction when working backwards through an equation.