Question

Solve the following equation.
$6\left( 3x+2 \right)-5\left( 6x-1 \right)=3\left( x-8 \right)-5\left( 7x-6 \right)+9x$

Answer 1

Hint: In this problem we need to solve the given equation that means we need to calculate the value of $x$ which satisfies the given equation. For this we will consider the LHS and RHS part of the given equation individually. Now we will simplify the LHS and RHS by applying some basic mathematical operations such as the distribution law of multiplication. After simplifying the LHS and RHS we will equate both of them and simplify the equation by transferring all the variables at one side and all the numerical at one side to get the required result.

Complete step-by-step solution:
Given equation is
$6\left( 3x+2 \right)-5\left( 6x-1 \right)=3\left( x-8 \right)-5\left( 7x-6 \right)+9x$.
LHS of the above equation is $6\left( 3x+2 \right)-5\left( 6x-1 \right)$ .
The RHS of the above equation is $3\left( x-8 \right)-5\left( 7x-6 \right)+9x$ .
Consider the LHS of the given equation which is $6\left( 3x+2 \right)-5\left( 6x-1 \right)$. Distribution law of multiplication says that $a\left( b\pm c \right)=ab\pm ac$ . Applying this formula in the LHS and simplifying it, then we will get
$\begin{align}
  & 6\left( 3x+2 \right)-5\left( 6x-1 \right)=6\times 3x+6\times 2-5\times 6x-5\left( -1 \right) \\
 & \Rightarrow 6\left( 3x+2 \right)-5\left( 6x-1 \right)=18x+12-30x+5 \\
 & \Rightarrow 6\left( 3x+2 \right)-5\left( 6x-1 \right)=-12x+17 \\
\end{align}$
Consider the RHS of the given equation which is $3\left( x-8 \right)-5\left( 7x-6 \right)+9x$. Applying distribution law of multiplication, some basic mathematical operation and simplifying the RHS, then we will have
$\begin{align}
  & 3\left( x-8 \right)-5\left( 7x-6 \right)+9x=3\times x+3\left( -8 \right)-5\times 7x-5\left( -6 \right)+9x \\
 & \Rightarrow 3\left( x-8 \right)-5\left( 7x-6 \right)+9x=3x-24-35x+30+9x \\
 & \Rightarrow 3\left( x-8 \right)-5\left( 7x-6 \right)+9x=-23x+6 \\
\end{align}$
Now equating the both simplified LHS and RHS, then we will get
$-12x+17=-23x+6$
Shifting the $-23x$ from RHS to LHS by interchanging the sign as well as the numerical $17$ from LHS to RHS by interchanging the sign, then we will have
$\begin{align}
  & -12x+23x=6-17 \\
 & \Rightarrow 11x=-11 \\
\end{align}$
Dividing the above equation with $11$ on both sides, then we will get
$\begin{align}
  & \dfrac{11x}{11}=-\dfrac{11}{11} \\
 & \Rightarrow x=-1 \\
\end{align}$
Hence the solution of the given equation $6\left( 3x+2 \right)-5\left( 6x-1 \right)=3\left( x-8 \right)-5\left( 7x-6 \right)+9x$ is $x=-1$ .

Note: In this problem we have only asked to calculate the solution of the given equation. Sometimes they may ask to check your solution or justify your solution. Then we need to substitute the calculated value of $x$ in the given equation and check whether the equation returns a value of zero or not. If it gives zero value then our solution is correct otherwise our solution is wrong.