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Algebraic equations are mathematical statements that show the relationship between different quantities. They often include variables, which are symbols that represent unknown values. In our example, the equation is given as:\(P = 4s\)Here, \(P\) and \(s\) are variables. The equation states that \(P\) is equal to four times \(s\). Understanding how to work with these equations is essential because they form the basis of many mathematical problems. Using algebraic equations, we can find unknown values and solve complex problems by manipulating these relationships logically.

Isolating the variable is a crucial step when solving algebraic equations. It means getting the variable by itself on one side of the equation. This allows us to find its value. In our example, we are asked to solve for \(s\) in the equation:\(P = 4s\)To isolate \(s\), follow these steps:

• Identify the variable you need to isolate, which is \(s\) in this problem.
• Perform an operation that leaves \(s\) alone on one side of the equation. Here, we divide both sides of the equation by 4 to isolate \(s\).

After performing the division, the equation becomes:\(\frac{P}{4} = s\)Now, \(s\) is isolated and we have successfully solved for the variable.

Mathematical operations such as addition, subtraction, multiplication, and division are essential tools for solving equations. In our example, we used division to isolate the variable \(s\). Here's a quick look at this process:The original equation is:\(P = 4s\)To solve for \(s\), we need to reverse the multiplication by 4. This is done through division, as dividing by a number is the inverse operation of multiplying by that same number:\(\frac{P}{4} = s\)Now, \(s\) is alone on one side of the equation. By understanding and applying these operations, we can manipulate equations to reveal the values of unknown variables. Practicing these operations often will help you become more comfortable with solving algebraic equations.