Question

Solve the linear equation: $2z - 1 = 14 - z$

Answer 1

Hint: We have to find the value of z in the equation given to us $2z - 1 = 14 - z$. The value of the variable can be found by using the method of transposition. Method of transposition involves doing the exact same mathematical thing on both sides of an equation with the aim of simplification in mind. This method can be used to solve various algebraic equations like the one given in question with ease.

Complete step-by-step solution:
We would use the method of transposition to find the value of z in $2z - 1 = 14 - z$. Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding the value of the required parameter.
Now, In order to find the value of z, we need to isolate z from the rest of the parameters.
So, $2z - 1 = 14 - z$
Taking all the terms consisting x to left side of the equation and all the constant term to the right side of equation, we get,
$ \Rightarrow $$2z + z = 14 + 1$
Adding up the like terms and simplifying the calculations,
$ \Rightarrow $$3z = 15$
Dividing both sides of the equation by $3$, we get,
$ \Rightarrow $$z = \dfrac{{15}}{3} = 5$
Hence, the value of z in $2z - 1 = 14 - z$ is $5$.

Note: If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal. The given problem deals with algebraic equations. There is no fixed way of solving a given algebraic equation. Algebraic equations can be solved in various ways. Linear equations in one variable can be solved by the transposition method with ease.