Problem 79 - Algebra 1

Question

Solve the equation. $$x-2=28$$

Step-by-Step Solution

Answer

The solution to the equation is \(x = 30\).

Step 1: Identify the Equation

The equation given is \(x - 2 = 28\)

Step 2: Isolate the variable

To isolate the variable 'x', add 2 to both sides of the equation. This is achieved due to the Additive Property of Equality. This results in \(x - 2 + 2 = 28 + 2\)

Step 3: Simplify the equation

Simplifying the equation will give the solution. Doing the addition on both sides results in \(x = 30\)

Key Concepts

Additive Property of Equality

The additive property of equality is a fundamental concept in solving linear equations. This property states that you can add the same number to both sides of an equation without changing the equation's equality. Imagine an old-fashioned balance scale. If you add equal weight to both sides, the balance remains level. In the context of our given problem, the equation is \(x - 2 = 28\). To solve for \(x\), we used this property and added 2 to both sides of the equation. This action keeps the equation balanced and allows us to more easily isolate the variable. In mathematical operations, the additive property of equality helps maintain the integrity of the equation as you work toward finding the solution.

• Keep in mind that what you do to one side of the equation, you must also do to the other.
• This ensures that both sides remain equal, preserving the equation's balance.

Isolation of Variables

The isolation of variables is a key strategy in solving equations. Its goal is to get the unknown variable by itself on one side of the equation. By isolating the variable, you can clearly see what number it is equivalent to. Let's look at our equation: \(x - 2 = 28\).

The variable \(x\) needs to be isolated. To accomplish this, we need to remove the -2. By adding 2 to both sides (using the additive property), the -2 is canceled out, leaving \(x\) by itself on one side: \(x = 28 + 2\). The operation of adding or subtracting is chosen based on what will effectively obtain \(x\) alone. Once the variable is isolated, the next step is to simplify the equation to find its value.

• Remember that the goal is to isolate the variable.
• Use inverse operations, such as addition or subtraction, to remove constants from the side of the equation with the variable.

Simplification of Equations

Simplification of equations is often the final step in solving linear equations, where the equation is made as simple as possible to find the answer easily. Once the variable is isolated, you need to simplify the numbers on either side to get the solution of the variable—let's revisit the equation: \(x = 28 + 2\).

By performing the addition, we arrive at \(x = 30\). At this point, the equation is simple, and we have found our solution.

• Double-check your math to ensure the simplified equation is correct.
• Once simplified, the equation should clearly show the value of the variable.

Remember, the goal of simplification is to make the equation as straightforward as possible so that the solution is apparent and easy to verify.