Question

How do you solve $ 5x+2=3\left( x+6 \right) $ ?

Answer 1

Hint: First of all, multiply 3 on the R.H.S of the given equation. After that, find the degree of the variable x. Then accumulate the variable terms on the one side of the equation and constants on the right-hand side of the equation. We know that constants are just numbers with no variable multiplied with them.

Complete step by step answer:
The equation given in the above problem is as follows:
 $ 5x+2=3\left( x+6 \right) $
Multiplying 3 with the terms written in the bracket one by one we get,
 $ \begin{align}
  & 5x+2=3x+3\left( 6 \right) \\
 & \Rightarrow 5x+2=3x+18........Eq.(1) \\
\end{align} $
Now, as you can see that degree of the variable x is 1. Degree is the highest power of the variable given and the variable in the above equation is x so the highest power which we can see of x is 1. Hence, the equation given above is a linear equation in one variable.
To solve this equation, we club the terms with variable x on one side of the equation and the constants on another side of the equation.
Subtracting $ 3x $ on both the sides of eq. (1) we get,
 $ 5x-3x+2=3x-3x+18 $
 $ 3x $ will be cancelled out on R.H.S of the above equation we get,
 $ 2x+2=18 $
Subtracting 2 on both the sides we get,
 $ 2x+2-2=18-2 $
+2 and -2 written on the L.H.S of the above equation will be cancelled out and we get,
 $ 2x=16 $
Dividing 2 on both the sides we get,
 $ \begin{align}
  & x=\dfrac{16}{2} \\
 & \Rightarrow x=8 \\
\end{align} $
Hence, we have got the solution of the given equation as 8.

Note:
 You can check the value of x that we have got above by substituting the value of x in the original equation given in the above problem and see if this value of x is satisfying the original equation or not.
The original equation given in the above problem is:
 $ 5x+2=3\left( x+6 \right) $
Now, substituting the value of x as 8 in the above equation we get,
 $ \begin{align}
  & 5\left( 8 \right)+2=3\left( 8+6 \right) \\
 & \Rightarrow 40+2=3\left( 14 \right) \\
 & \Rightarrow 42=42 \\
\end{align} $
As you can see that L.H.S = R.H.S so the value of x that we have found above is absolutely correct.