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# How do you solve the linear equation $7x-\left( x-3 \right)=3\left( x+10 \right)$ ?

Last updated date: 04th Aug 2024
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Answer
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Hint: From the question given, we have been asked to solve $7x-\left( x-3 \right)=3\left( x+10 \right)$ for getting the value of $x$ . For that we need to use basic arithmetic simplifications like addition and transformations like shifting from right hand side to left hand side and reduce it. We can get the solution of the equation.

Complete step-by-step solution:
Now considering from the question we have been asked to solve the given equation $7x-\left( x-3 \right)=3\left( x+10 \right)$ for getting the value of $x$.
For doing that we need to use basic arithmetic simplifications like addition and transformations like shifting from right hand side to left hand side and reduce it.
Firstly we will simplify the given equation as follows
\begin{align} & 7x-\left( x-3 \right)=3\left( x+10 \right) \\ & \Rightarrow 7x-x+3=3x+30 \\ & \Rightarrow 6x+3=3x+30 \\ \end{align}
Here we will shift all the terms except the term involving $x$ in it to one side and keep that respective term in one side. For that here we will shift $3x$ from right hand to left hand side. After doing that we will have
\begin{align} & \Rightarrow 6x-3x+3=30 \\ & \Rightarrow 6x-3x=30-3 \\ \end{align} .
Now as we need the value of $x$ we will perform the basic simple arithmetic subtraction on the both sides after that we will have $\Rightarrow 3x=27$ .
Now we will divide with $3$on both sides after that we will have
\begin{align} & \Rightarrow \dfrac{3x}{3}=\dfrac{27}{3} \\ & \Rightarrow x=9 \\ \end{align}
Therefore we can conclude that the value of $x$ obtained from the given equation $7x-\left( x-3 \right)=3\left( x+10 \right)$ is $9$.

Note: We should be very careful while doing the calculation in this problem. Also, we should be very careful while solving the equation. Also, we should be very careful while transforming the equation. Also, we should do exact transformations to the given equation to obtain the perfect answer. This type of questions are very easy and do not require much calculations so the possibility of mistakes in questions of this type are very less. Similarly we can solve any other equations like for the equation $5x-4=3x-6$ the value of $y$ will be given as $\Rightarrow 2x=-2\Rightarrow x=-1$ .