How do you simplify $7\left( 6x+8 \right)$?

Hint: We multiply the coefficients of the given terms of $\left( 6x+8 \right)$ with 7. The sign of the coefficient’s does not change. We place an arbitrary value for x and verify the result of the equation.The main change is the change of coefficients being multiplied from 7.

Complete step by step solution:
The given equation $7\left( 6x+8 \right)$ is a linear equation of x. we need to simplify for the coefficients that are present in front of the term $\left( 6x+8 \right)$.
All the main coefficients will be multiplied by 7.
As it is a positive number the sign will not change
The individual terms in $\left( 6x+8 \right)$ are both positive.
Multiplying them with 7 gives $7\times 6=42$ and $7\times 8=56$ respectively.
Therefore, we have the final solution as
$\begin{align}
  & 7\left( 6x+8 \right) \\
 & =7\times 6x+7\times 8 \\
 & =42x+56 \\
\end{align}$.
Now we verify the solution by putting a value for x. let’s take $x=2$.
Therefore, the left-hand side of the equation becomes
$7\left( 6x+8 \right)=7\left( 6\times 2+8 \right)=7\times 20=140$
The right-hand side of the equation is $42x+56=42\times 2+56=84+56=140$.
Thus, verified the equation $7\left( 6x+8 \right)=42x+56$.

Note: The value of the coefficient’s changes. No value for the variable is changed due to the multiplication of the coefficients. The process of multiplication and division both work similarly.