Question

Solve
\[5\left( {1 - 2x} \right) = 9\left( {1 - x} \right)\]

Answer 1

Hint: First we need to expand the brackets. Then we will have a linear equation with one variable. We can solve this using shifting the variables on one side of the equations and the constants on the other side. That is we can solve this using the transposition method.

Complete step-by-step answer:
Given, \[5\left( {1 - 2x} \right) = 9\left( {1 - x} \right)\].
Expanding the brackets on both sides of the equation, then we have:
\[5 - 10x = 9 - 9x\]
We transpose ‘5’ which is present on the left-hand side of the equation to the right-hand side of the equation by subtracting ‘5’ on the right-hand side of the equation.
\[ - 10x = 9 - 9x - 5\]
Similarly, we transpose ‘-9x’ to the left-hand side of the equation by adding ‘9x’ on the left-hand side of the equation.
\[ - 10x + 9x = 9 - 5\]
Thus we have a variable and constants are separated.
\[ - x = 4\]
\[ \Rightarrow x = - 4\].This is the required answer.

Note: To verify the obtained answer we can substitute the obtained value in the given equation. If we obtained LHS is equal to RHS then our obtained answer is correct.
\[5\left( {1 - 2x} \right) = 9\left( {1 - x} \right)\]
\[5\left( {1 - 2\left( { - 4} \right)} \right) = 9\left( {1 - \left( { - 4} \right)} \right)\]
\[5\left( {1 + 8} \right) = 9\left( {1 + 4} \right)\]
\[5\left( 9 \right) = 9\left( 5 \right)\]
Simplifying we have,
\[ \Rightarrow 45 = 45\].
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.