91Ó°ÊÓ

When solving equations with decimal coefficients, one of the first steps is distributing the coefficients to each term inside parentheses. This means you multiply the coefficient by each term within the parentheses. For example, in the expression \(0.10(n + 7)\), you distribute the 0.10 to both \(n\) and 7.

This step transforms the equation into:
\ 0.10n + 0.10 \times 7 \
Simplified, this gives:
\ 0.10n + 0.70\
Now, you can incorporate this expression back into the original equation to make it easier to solve as per the example provided: \(0.05 n + 0.10(n + 7) = 3.55\) becomes \(0.05 n + 0.10 n + 0.70 = 3.55\). Distributing coefficients is essential for simplifying the equation and progressing towards the solution.

Once the coefficients have been distributed, the next step is to combine like terms. Like terms are terms that contain the same variable raised to the same power. In our example, \(0.05 n\) and \(0.10 n\) are like terms because they both include the variable \(n\).

To combine like terms, add their coefficients together:
\0.05 n + 0.10 n \
This yields:
\0.15 n\.
So, the equation now becomes \(0.15 n + 0.70 = 3.55\).

Combining like terms simplifies the equation further, making it easier to tackle the subsequent steps.

The final main concept is isolating the variable. In our target equation, \(0.15 n + 0.70 = 3.55\), the goal is to get \(n\) by itself on one side of the equation.

Start by subtracting the constant term (0.70) from both sides of the equation:
\ 0.15 n = 3.55 - 0.70 \
Which simplifies to:
\0.15 n = 2.85\.
Finally, solve for \(n\) by dividing both sides by the coefficient of \(n\) (which is 0.15):
\ n = \frac{2.85}{0.15} \
Simplify the division to find \(n = 19\).
By isolating the variable, you solve for its value, completing the equation.