Question

How do you simplify $8\left( 3x-5 \right)-6x$ ?

Answer 1

Hint: For simplifying the given question, first of all we will open the bracket, after that we have to multiply the digit or variable that is outside of the bracket to the digits or variables that were in the bracketed previously. So, we will get the expansion of the equation. Now, we will add or subtract like terms. Hence, we will get the simplified value of the given question.

Complete step by step solution:
The given equation is $8\left( 3x-5 \right)-6x$ .
Now, we will divide the given equation into two parts to make the solution simple as:
$\Rightarrow 8\left( 3x-5 \right)$ … $\left( i \right)$
And
$\Rightarrow \left( -6x \right)$ … $\left( ii \right)$
In which firstly we will solve the bracketed portion of the question as:
$\Rightarrow 8\left( 3x-5 \right)$
Since, the above equation has brackets, we will have to open the bracket. Since, we will open the bracket that means we will multiply $8$ to $3x$ and $5$ respectively as:
$\Rightarrow 8\times 3x-8\times 5$
Here, we will have the value after multiplication by $8$ as:
$\Rightarrow 24x-40$ … $\left( iii \right)$
Since, equation $\left( ii \right)$ has nothing to solve, we will write it as it is supposed as:
$\Rightarrow \left( -6x \right)$
Now, combining the equation $\left( iii \right)$ and equation $\left( ii \right)$as:
$\Rightarrow \left( 24x-40 \right)+\left( -6x \right)$
Let us simplify the above equation as:
$\Rightarrow 24x-40-6x$
Here $24x$ and $6x$ are like terms. So, we can add or subtract this terms as
$\begin{align}
  & \Rightarrow 24x-6x-40 \\
 & \Rightarrow \left( 24-6 \right)x-40 \\
\end{align}$
After subtracting the above equation, we will find the value of the given question as:
$\Rightarrow 18x-40$

Hence, the simplified value of the given equation $8\left( 3x-5 \right)-6x$ is $18x-40$

Note: We can check if the simplified value of the given equation is correct or not in reverse way as:
Since, we have simplified value the given question as:
$\Rightarrow 18x-40$
We can write it as:
$\Rightarrow \left( 24x-6x-40 \right)$
Now, we will separate the terms of above equation so that we can get two terms as:
$\Rightarrow \left( 24x-40 \right)-6x$
Here, $8$ is a common number for the bracketed term. So we can write it in the term of multiple of $8$ as:
$\Rightarrow \left( 8\times 3x-8\times 5 \right)-6x$
Now, we will take out this common number from the bracket as:
$\Rightarrow 8\left( 3x-5 \right)-6x$
Now, we got the given equation from the simplified value of the given question. Hence, the solution is correct.