Question

How do you solve the linear equation \[4\left( x+3 \right)=3x-10\]?

Answer 1

Hint: Remove the bracket by multiplying the constant term 4 with each term inside the bracket present in the L.H.S. Now, rearrange the terms of the given equation by taking the terms containing the variable x to the L.H.S. and taking the constant terms to the R.H.S. Use the arithmetic operations to simplify the equation. Make the coefficient of x equal to 1 and accordingly change the R.H.S. to get the answer.

Complete step by step solution:
Here, we have been provided with the equation: \[4\left( x+3 \right)=3x-10\] and we are asked to solve this equation. That means we have to find the value of x.
\[\because 4\left( x+3 \right)=3x-10\]
Multiplying the constant 4 with each term inside the bracket in the L.H.S we get,
\[\Rightarrow 4x+12=3x-10\]
We can see that the given equation is a linear equation in one variable which is x. So, taking the terms containing the variable x to the L.H.S. and taking the constant terms to the R.H.S., we get,
\[\begin{align}
  & \Rightarrow 4x-3x=-10-12 \\
 & \therefore x=-22 \\
\end{align}\]
Hence, the value of x is -22.

Note: Here we have been provided with a single equation only because we have to find the value of a single variable (x). So, in general if we have to solve an equation having ‘n’ number of variables then we should be provided with ‘n’ number of equations. You can check the answer by substituting the obtained value of x in the equation provided in the question. You have to determine the value of L.H.S. and R.H.S. separately and if they are equal then our answer is correct.