Question

How do you solve $-4\left( x+10 \right)-6=-3\left( x-2 \right)$?

Answer 1

Hint: To solve the above equation $-4\left( x+10 \right)-6=-3\left( x-2 \right)$ we are going to first open the bracket on both the sides and then rearrange this equation in such a way so that x will be on one side of the equation and all the constants on the other side of the equation. And then further simplify the expression to get the value of x.

Complete step by step answer:
The equation given in the above problem of which we have to solve is as follows:
$-4\left( x+10 \right)-6=-3\left( x-2 \right)$
In the above equation, opening the bracket on both the sides by multiplying -4 by $\left( x+10 \right)$ and -3 by $\left( x-2 \right)$ and we get,
$\begin{align}
  & -4x-4\left( 10 \right)-6=-3x-3\left( -2 \right) \\
 & \Rightarrow -4x-40-6=-3x+6 \\
 & \Rightarrow -4x-46=-3x+6 \\
\end{align}$
Now, writing the expressions of x on one side of the equation and constants on the other side of the equation by adding 4x on both the sides and we get,
$\begin{align}
  & -4x+4x-46=-3x+4x+6 \\
 & \Rightarrow 0-46=x+6 \\
\end{align}$
Subtracting 6 on both the sides we get,
$\begin{align}
  & -46-6=x+6-6 \\
 & \Rightarrow -52=x \\
\end{align}$
From the above calculations, we have solved the value of x as -52.

Hence, the solution of the given equation is equal to -52.

Note: You can check if the value of x that you have calculated above is correct or not by substituting the value of x that we have calculated in the above equation.
The value of x that we have calculated above is -52. Substituting this value of x in the given equation we get,
$\begin{align}
  & -4\left( x+10 \right)-6=-3\left( x-2 \right) \\
 & \Rightarrow -4\left( -52+10 \right)-6=-3\left( -52-2 \right) \\
 & \Rightarrow -4\left( -42 \right)-6=-3\left( -54 \right) \\
 & \Rightarrow 168-6=162 \\
 & \Rightarrow 162=162 \\
\end{align}$
In the above calculations, you can see that by substituting the value of x as -52 in the given equation we are getting the L.H.S equal to R.H.S. This means that the value of x that we have solved above is correct because it is satisfying the given equation.