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Understanding the subtraction property of equality is crucial when solving equations. This property tells us that if we have an equation, we can safely subtract the same value from both sides without changing the equation's balance. Much like a balanced scale, if you take away the same weight from both sides, the scale remains balanced.

In the example given, the original equation is \(x + 5 = 12\). To isolate \(x\), which means to get \(x\) on its own on one side of the equation, we subtract 5 from both sides. This operation is justified by the subtraction property of equality. Here's the breakdown:

• Starting equation: \(x + 5 = 12\)
• Subtract 5 from both sides: \(x + 5 - 5 = 12 - 5\)
• Simplify the equation: \(x = 7\)

Each step is consistent with keeping the equation balanced, making this property essential in maintaining equality.

Solving equations may seem scary at first, but it can be as simple as following an orderly series of steps. The goal is to manipulate the equation to isolate the variable, like \(x\), on one side. This means you perform operations that simplify or transform the equation without changing its equality.

In our example, the given equation is \(x + 5 = 12\). We only need one operation:

• Subtract 5 from both sides to begin isolating \(x\).

The process of solving this equation involves simplifying each side. By doing so, not only are we isolating \(x\), but we also transform the equation into a much simpler one: \(x = 7\). This straightforward approach allows for clarity and accuracy while solving many types of equations.

When solving equations, it's important to explain each step logically. This ensures that your reasoning is clear, allowing others to follow your process without confusion. Every time you perform an action on an equation, such as subtraction or addition, you should justify it with a mathematical property.

In the exercise provided, the subtraction of 5 from both sides is justified by the subtraction property of equality. This means:

• Subtracting the same value keeps the equation balanced.
• This mathematical property is universally accepted and applies to all equations.

Using such justifications not only strengthens your understanding, but it also makes verifying your solution much easier. It's like having proof for every action you take, leaving no room for doubt or error.