## 4x=10 What is x?

To solve for x in the equation 4x = 10, follow these steps:

- Divide both sides of the equation by 4: 4x/4 = 10/4.
- Simplify: x = 10/4.
- Further simplify by dividing the numerator and denominator by their greatest common factor, which is 2: x = (10/2)/(4/2).
- Calculate: x = 5/2.
So, x = 5/2.

## Solving a One-Step Linear Equation

In algebra, linear equations with one variable represent mathematical relationships where the value of the variable makes the equation true. Solving these one-step linear equations relies on using inverse operations to isolate the variable term.

Let’s examine solving the equation 4x = 10 step-by-step:

Analyzing the Equation

4x = 10

This linear equation features:

- The coefficient 4 multiplied by the variable x
- The constant value 10 on the other side
- We need to find the value of x that makes this equation true

## Using Inverse Operations

To isolate x, we can apply an inverse operation:

4x = 10 Divide both sides by 4: x = 10/4

Dividing by 4 “undoes” the multiplication by 4, leaving just x by itself.

Simplifying the Solution

10/4 = 2.5

Therefore, the solution is: x = 2.5

## Checking the Solution

We can verify x = 2.5 satisfies the original equation:

4(2.5) = 10 10 = 10 ✅

The two sides are equal, so x = 2.5 is the correct solution.

In summary, isolating variables in linear equations uses inverse operations. Dividing both sides by the coefficient undoes the multiplication to solve for the unknown variable. Checking the solution confirms the algebra is accurate.

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