Q. 380 - Intermediate Algebra

Question

Simplify the following expression using the distributive property.

$7\left(3n+9\right)-\left(4n-13\right)$

Step-by-Step Solution

Answer

The expression $7\left(3n+9\right)-\left(4n-13\right)$ can be written as $17n+76$.

Step 1. Given expression.

The given expression is $7\left(3n+9\right)-\left(4n-13\right)$.

Step 2. Formula used.

The distributive property is shown below.

If a, b, c are real numbers then $a\left(b+c\right)=ab+ac$.

Step 3. Apply the distributive property.

Apply the distributive property to the given expression as follows.

$$\begin{gathered} 7\left(3n+9\right)-\left(4n-13\right)=7\left(3n\right)+7\left(9\right)-\left(4n\right)-\left(-13\right) \\ 7\left(3n+9\right)-\left(4n-13\right)=21n+63-4n+13 \\ 7\left(3n+9\right)-\left(4n-13\right)=17n+76 \end{gathered}$$

Step 4. Conclusion.

The expression $7\left(3n+9\right)-\left(4n-13\right)$ can be simplified as $17n+76$.