91Ó°ÊÓ

Solving an equation typically involves finding the value of the variable that makes the equation true. In the problem at hand, we deal with a linear equation: \(2x = 10\). Linear equations are mathematical statements of equality that involve variables raised to the power of one. Solving such equations is part of basic algebra and requires performing operations to simplify and manipulate the equation. When working to solve any equation, always keep your end goal in mind: find the value for the unknown that satisfies the equation. Here's how you typically approach solving equations:

• Identify the equation and unknown variable.
• Perform operations that help isolate the variable on one side of the equation.
• Simplify each step to make the process clearer.

Eventually, the aim is to have the variable by itself on one side, revealing its value on the other side.

Isolating the variable is a crucial step in solving equations. The goal here is to get the variable, in this case, \(x\), by itself on one side of the equation, so we can see what it's equal to. Let's break down the process:

• First, look at the equation you have: \(2x = 10\).
• Your task is to manipulate the equation such that all terms containing \(x\) are on one side, with the constant term on the other.

This might involve performing opposite operations to "undo" any effects that are preventing \(x\) from standing alone. Here, since \(x\) is multiplied by 2, you will perform division to isolate \(x\). Once isolated, you can easily determine its value.

The division property of equality is essential for isolating variables. This principle states that dividing both sides of an equation by the same non-zero number will preserve equality. It is particularly helpful when you have a variable multiplied by a number, as seen in \(2x = 10\). Here's how it works:

• You need to isolate \(x\) by canceling out the number multiplied with it, which is done by dividing.
• Divide each side of the equation by 2: \(\frac{2x}{2} = \frac{10}{2}\).
• Simplify both sides to reach the solution: \(x = 5\).

Remember, whatever operation you do on one side, you must also do on the other. This keeps the equation balanced and true. It is a fundamental strategy for maintaining the equality while simplifying and solving the equation.