Question

How do you solve \[2\left( 4z-1 \right)=3\left( z+2 \right)\]?

Answer 1

Hint: Remove the bracket by multiplying the factors with each term inside the bracket on both sides separately. Now, take the terms containing the variable ‘z’ to the left-hand side and the constant terms to the right-hand side. Apply simple mathematical operations like addition, subtraction, multiplication, and division, whichever needed to simplify the equation. Find the value of ‘z’ to get the answer.

Complete step by step answer:
Here, we have been provided with the equation: \[2\left( 4z-1 \right)=3\left( z+2 \right)\] and we are asked to solve this equation. That means we have to find the value of z.
Clearly, we can see that the given equation is a linear equation in one variable which is ‘z’, so now removing the bracket by multiplying the factor with the respective terms, we get,
\[\Rightarrow 8z-2=3z+6\]
Now, taking the terms containing the variable ‘z’ to the left-hand side (L.H.S) and the constant terms to the right-hand side (R.H.S), we get,
\[\begin{align}
  & \Rightarrow 8z-3z=6+2 \\
 & \Rightarrow 5z=8 \\
\end{align}\]
Dividing both sides with 5, we get,
\[\begin{align}
  & \Rightarrow \dfrac{5z}{5}=\dfrac{8}{5} \\
 & \Rightarrow z=\dfrac{8}{5} \\
\end{align}\]
Hence, the value of z is \[\dfrac{8}{5}\].

Note:
 One may note that we have been provided with a single equation only. The reason is that we have to find the value of only one variable, that is z. So, if we have to solve an equation having ‘n’ number of variables then we should be provided with ‘n’ equations. Now, one can check the answer