Calculate for Unknown X 2 X 200 0.5 230

This guide explains how to solve for the unknown variable x in the equation 2x + 200 = 0.5x + 230. We'll cover the step-by-step process, provide a worked example, and include an interactive calculator to verify your results.

How to Solve for Unknown x

Solving for x in a linear equation involves isolating the variable on one side of the equation. Here's the general approach:

Start with the equation: 2x + 200 = 0.5x + 230
Subtract 0.5x from both sides to get all x terms on one side
Subtract 200 from both sides to isolate the constant terms
Divide both sides by the coefficient of x to solve for x

Formula Used

The general solution for equations of the form ax + b = cx + d is:

x = (d - b) / (a - c)

Step-by-Step Solution

Let's solve the equation 2x + 200 = 0.5x + 230 step by step:

Subtract 0.5x from both sides:
2x - 0.5x + 200 = 230

1.5x + 200 = 230
Subtract 200 from both sides:
1.5x = 230 - 200

1.5x = 30
Divide both sides by 1.5:
x = 30 / 1.5

x = 20

Important Note

When solving equations, always perform the same operation on both sides to maintain equality. This ensures the solution remains valid.

Worked Example

Let's verify our solution with a different set of numbers. Suppose we have the equation 3x + 150 = 1.5x + 180.

Subtract 1.5x from both sides:
3x - 1.5x + 150 = 180

1.5x + 150 = 180
Subtract 150 from both sides:
1.5x = 180 - 150

1.5x = 30
Divide both sides by 1.5:
x = 30 / 1.5

x = 20

In both cases, we arrive at x = 20, demonstrating the consistency of the solution method.

Frequently Asked Questions

What if the coefficients of x are the same on both sides?: If the coefficients are identical, the equation will simplify to a statement about constants. For example, 2x + 5 = 2x + 10 simplifies to 5 = 10, which is false, meaning there's no solution.
Can I solve for x if the equation has decimals?: Yes, you can solve for x with decimal coefficients. The process remains the same: isolate the x terms and constants, then divide by the coefficient of x.
What if the equation has negative coefficients?: Negative coefficients work the same way as positive ones. Just be careful with the signs when subtracting terms. For example, in -2x + 10 = -x + 5, you would add x to both sides first.
How do I know if my solution is correct?: Substitute your solution back into the original equation to verify. If both sides equal the same value, your solution is correct.