0.012 X 2 0.40-X Solve for X Calculator

This calculator solves the linear equation 0.012x + 2 - 0.40x = 0 for x. Learn how to solve it manually, understand the formula, and see practical examples.

How to Solve 0.012x + 2 - 0.40x = 0

Solving linear equations is a fundamental math skill used in algebra, physics, engineering, and many other fields. Here's how to solve the equation 0.012x + 2 - 0.40x = 0:

Combine like terms (terms with the same variable)
Isolate the variable term
Solve for the variable by dividing both sides by its coefficient

This equation has one solution because it's a linear equation with one variable. The solution is valid for all real numbers.

Step-by-Step Solution

Let's solve the equation 0.012x + 2 - 0.40x = 0 step by step:

Combine like terms

First, combine the terms with x:

0.012x - 0.40x + 2 = 0

(0.012 - 0.40)x + 2 = 0

-0.388x + 2 = 0
Isolate the variable term

Subtract 2 from both sides to move the constant term:

-0.388x + 2 - 2 = 0 - 2

-0.388x = -2
Solve for x

Divide both sides by -0.388 to isolate x:

x = -2 / -0.388

x ≈ 5.155

The solution to the equation is x ≈ 5.155. This means when x is approximately 5.155, the equation holds true.

The Formula

The general form of a linear equation in one variable is:

ax + b = 0

Where:

a is the coefficient of x
b is the constant term
x is the variable to solve for

For our specific equation 0.012x + 2 - 0.40x = 0, we can rewrite it in the standard form:

-0.388x + 2 = 0

The solution is then:

x = -b / a

Worked Example

Let's solve a similar equation to reinforce the method: 0.05x + 3 - 0.15x = 0

Combine like terms

0.05x - 0.15x + 3 = 0

-0.10x + 3 = 0
Isolate the variable term

-0.10x = -3
Solve for x

x = -3 / -0.10

x = 30

In this example, x = 30. This shows how the method applies to similar equations with different coefficients.

FAQ

What if the equation has no solution?: Linear equations in one variable always have exactly one solution unless they are in the form 0 = c (where c ≠ 0), which has no solution.
Can I solve equations with fractions using this method?: Yes, you can convert fractions to decimals or use the same method with fractions. The process is similar but may involve more complex arithmetic.
What if the coefficient of x is negative?: The sign of the coefficient doesn't affect the method. You'll get a negative solution if the constant term is positive and vice versa.
How do I check if my solution is correct?: Substitute your solution back into the original equation to verify it holds true. For x ≈ 5.155, plugging it back should make both sides equal.
Can I use this method for equations with more than one variable?: No, this method only works for linear equations with one variable. For multiple variables, you would need additional equations or methods like substitution or elimination.