Solve 8 = 2x + 4.
The Correct Answer and Explanation is:
To solve the equation (8 = 2x + 4), we want to isolate the variable (x). Here’s a step-by-step explanation of how to do this:
- Understand the Equation: The equation consists of two sides, where the left side equals 8, and the right side is a linear expression (2x + 4). Our goal is to find the value of (x) that makes this equation true.
- Subtract 4 from Both Sides: To begin isolating (x), we need to eliminate the constant on the right side. We do this by subtracting 4 from both sides of the equation:
[
8 – 4 = 2x + 4 – 4
]
Simplifying both sides gives:
[
4 = 2x
] - Divide Both Sides by 2: Now that we have (2x) on one side, we need to solve for (x) by dividing both sides of the equation by 2:
[
\frac{4}{2} = \frac{2x}{2}
]
This simplifies to:
[
2 = x
] - Conclusion: We have found that (x = 2).
- Verification: To ensure our solution is correct, we can substitute (x) back into the original equation:
[
8 = 2(2) + 4
]
Simplifying the right side gives:
[
8 = 4 + 4
]
Since both sides equal 8, our solution (x = 2) is indeed correct.
This problem illustrates basic algebraic principles, such as maintaining balance in an equation, isolating variables, and performing operations equally on both sides. The steps of addition and division are foundational operations in solving linear equations and are widely applicable in mathematics. Understanding these principles is essential for tackling more complex algebraic expressions and equations in the future.