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Solving equations means finding the value of the variable that makes the equation true. In this case, our task is to find the value of \(x\) in the equation \(7(x + 2) = 21\). Equation solving usually involves manipulating the equation so that the variable is isolated on one side. This requires a systematic approach of simplifying and following arithmetic operations.

In basic algebra, the goal is to transform the equation step by step. You want to reach a point where the equation looks like \(x = ...\). This clarity in approach helps tackle even more complex algebraic problems. Make sure to:

• Always perform the same operation on both sides of the equation.
• Move constants to one side and variables to the other.

The outcome is a clear and straightforward answer, showing the value of the unknown variable.

The distributive property is a fundamental rule in algebra that allows us to simplify and solve equations more efficiently. This property states that when you multiply a number by a sum, you can distribute the multiplication to each addend separately.

Consider our exercise: \(7(x + 2) = 21\). To use the distributive property, multiply 7 by both \(x\) and 2, giving us \(7x + 14\). This simplification makes further steps easier. Typically, you would:

• Identify the multiplication outside the parentheses.
• Apply the multiplication to each term inside the parentheses.

Using the distributive property correctly ensures simpler equations, allowing for more straightforward manipulation and solution.

Isolating the variable is key to solving equations because it leads to the discovery of the variable's value. In our exercise, after using the distributive property, you get \(7x + 14 = 21\). The next step is to isolate \(x\) by getting rid of the constant 14. Subtract 14 from both sides to get \(7x = 7\).

This process is crucial because it simplifies the equation to a form that can be easily solved for \(x\). When isolating variables, keep in mind to:

• First eliminate any constant in the equation.
• Divide or multiply to get the variable by itself.

By methodically isolating the variable, you transform the problem into a directly solvable format, making the algebraic process smooth and logical.