Question

Solve
\[\left( {7 \times 20} \right) - 8z = 0\]

Answer 1

Hint: In the given problem we need to solve this for ‘z’. We can solve this using the transposition method. First, we simplify the terms in brackets then we group the ‘z’ terms on one side and constants on the other side of the equation.

Complete step-by-step answer:
Given, \[\left( {7 \times 20} \right) - 8z = 0\].
\[140 - 8z = 0\]
We transpose ‘140’ which is present in the left hand side of the equation to the right hand side of the equation by subtracting ‘140’ on the right hand side of the equation.
\[ - 8z = - 140\]
Now dividing the whole equation by negative 8.
\[z = \dfrac{{ - 140}}{{ - 8}}\]
\[z = \dfrac{{70}}{4}\]
\[ \Rightarrow z = \dfrac{{35}}{2}\]. This is the exact form.
\[ \Rightarrow z = 17.5\].This is the decimal from.

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.
\[\left( {7 \times 20} \right) - 8z = 0\]
\[\left( {7 \times 20} \right) - 8\left( {\dfrac{{35}}{2}} \right) = 0\]
\[\left( {7 \times 20} \right) - \left( {4 \times 35} \right) = 0\]
\[140 - 140 = 0\]
Simplifying we have,
\[ \Rightarrow 0 = 0\].
That is LHS=RHS. Hence the obtained is correct.
In the above, we did the transpose of addition and subtraction. 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.