91Ó°ÊÓ

When solving equations, we often need to simplify expressions by combining like terms.
Like terms are terms that have the same variables raised to the same power. For instance, in the equation given, we have the terms $$0.48x$$ and $$0.58x$$ on opposite sides of the equation.
Both of these terms contain the variable $$x$$, making them like terms.

To combine them, we simply need to move all the like terms to one side of the equation.
We do this by using addition or subtraction. In the example, we subtract $$0.48x$$ from both sides to combine the $$x$$ terms on one side:
$$0.48x + 1.56 - 0.48x = 0.58x - 0.64 - 0.48x$$.
This simplifies to:
$$1.56 = 0.10x - 0.64$$.

By combining like terms, we make the equation simpler to solve in subsequent steps.

The next step in solving an equation is to isolate the variable.
The goal here is to get all the terms with the variable on one side and the constants on the other.
In our example, after combining like terms, we have:
$$1.56 = 0.10x - 0.64$$.

To isolate $$x$$, we need to undo whatever operations are being performed on it.
Begin by eliminating the constant term on the same side as the variable by adding $$0.64$$ to both sides:
$$1.56 + 0.64 = 0.10x - 0.64 + 0.64$$.

This leaves us with:
$$2.20 = 0.10x$$.

Now, the variable term is isolated, and we are ready for the next step.

With the variable isolated, the final step is to solve the linear equation.
A linear equation is one where the variable is raised to the power of one.
In our simplified equation:
$$2.20 = 0.10x$$,
we solve for $$x$$ by dividing both sides by the coefficient of $$x$$ (which is $$0.10$$):
$$x = \frac{2.20}{0.10}$$.

After performing the division, we find:
$$x = 22$$.

By following these steps, you can solve any linear equation with decimal coefficients.

Remember:

• Combine like terms to simplify.
• Isolate the variable to one side of the equation.
• Solve for the variable by performing the necessary arithmetic operations.