Question

Solve the linear equation \[2z + 3 = - 19\]?

Answer 1

Hint: In the given problem we need to solve this for ‘z’. We can solve this using the transposition method. The common transposition method is to do the same thing (mathematically) to both sides of the equation, with the aim of bringing like terms together and isolating the variable (or the unknown quantity). That is we group the ‘z’ terms on one side and constants on the other side of the equation.

Complete step-by-step solution:
Given, \[2z + 3 = - 19\].
We transpose \[3\] which is present in the left-hand side of the equation to the right-hand side of the equation by subtracting \[3\]on the right-hand side of the equation.
\[2z = - 19 - 3\]
\[\Rightarrow 2z = - 22\]
Transpose 2 to the right-hand side of the equation by dividing 2 on the right-hand side of the equation.
\[\Rightarrow z = - \dfrac{{22}}{2}\]
\[ \Rightarrow z = - 11\]. This is the required result.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘z’ in the given problem.
\[2z + 3 = - 19\]
\[\Rightarrow 2( - 11) + 3 = - 19\]
\[\Rightarrow - 22 + 3 = - 19\]
\[ \Rightarrow - 19 = 19\]
Hence the obtained answer is correct.
In the above, we did the transpose of addition. Similarly, if we have multiplication, we use division to transpose. If we have division, we use multiplication to transpose. Follow the same procedure for these kinds of problems.