How do you simplify $7x+4\left( x+5 \right)$?

Hint:We separate the variables and the constants of the equation $7x+4\left( x+5 \right)$. We apply the binary operation of addition and subtraction for both variables and constants. The solutions of the variables and the constants will be added at the end to get the final answer. We can also solve the simplified form of the expression for the given value of $a$ and find the value of the variable $x$.

Complete step by step solution:
The given equation $7x+4\left( x+5 \right)$ is an algebraic expression of $x$. We need to simplify the equation by solving the variables and the constants separately.

All the terms in the equation of $7x+4\left( x+5 \right)$ are either variable of $x$ or a constant. We
first separate the variables.

We break the multiplication by multiplying 4 with $\left( x+5 \right)$.
$4\left( x+5 \right)=4x+20$. The expression change from $7x+4\left( x+5 \right)$ to $7x+4x+20$

There are two variables which are $7x$ and $4x$.

The binary operation between them is addition which gives us $7x+4x=11x$.

Now we take the constants.

There is only one constant which is 20.

The final solution becomes
$\begin{align}
& 7x+4\left( x+5 \right) \\
& =7x+4x+20 \\
& =11x+20 \\
\end{align}$.

Now if we had to find the solution of the given equation being equal to $a$, then the equation
becomes $11x+20=a$. Here $a$ is constant.

Now we take the variable on one side and the constants on the other side.
\[\begin{align}
& 11x+20=a \\
& \Rightarrow 11x=a-20 \\
& \Rightarrow x=\dfrac{a-20}{11} \\
\end{align}\]
Therefore, the solution is \[x=\dfrac{a-20}{11}\].

Therefore, the simplified form of the expression $7x+4\left( x+5 \right)$ is $11x+20$.

Note: We can verify the result of the equation $7x+4\left( x+5 \right)=11x+20$ by taking the value of $x$ as $x=2$. Therefore, the left-hand side of the equation becomes
$7x+4\left( x+5 \right)=7\times 2+4\left( 2+5 \right)=14+4\times 7=42$ the right-hand side of the equation becomes $11x+20=11\times 2+20=22+20=42$ Thus, verified for the equation $7x+4\left( x+5 \right)=11x+20$.