Question

Solve the following equation
\[5\left( {2x - 3} \right) - 3\left( {3x - 7} \right) = 5\]

Answer 1

Hint: Here we need to find the value of ‘x’ which satisfies the given equation. Now we need to expand the brackets on the left-hand side of the equation. Then we need to add or subtract the like terms and constant terms on the left-hand side of the equation. Then to find the value of ‘x’ we use the transposition method.

Complete step-by-step solution:
Given, \[5\left( {2x - 3} \right) - 3\left( {3x - 7} \right) = 5\].
Now expand the brackets in LHS of the equation.
\[10x - 15 - 9x + 21 = 5\]
Now subtracting the like terms and constant on the left hand side of the equation we have,
\[x + 6 = 5\]
Thus we have a linear equation with one variable.
We transpose \[6\] which is present in the left-hand side of the equation to the right-hand side of the equation by Subtracting \[6\] on the right-hand side of the equation.
\[x = 5 - 6\]
\[ \Rightarrow x = - 1\].
This is the required answer.

Note: By simplifying we have obtained the answer for ‘x’. We can check whether the obtained value of ‘x’ is correct or not. To check we simply substitute the obtained value of ‘x’ in the given problem. If L.H.S is equal to R.H.S. then our answer is correct.
\[5\left( {2x - 3} \right) - 3\left( {3x - 7} \right) = 5\]
\[\Rightarrow 5\left( {2( - 1) - 3} \right) - 3\left( {3( - 1) - 7} \right) = 5\]
\[\Rightarrow 5\left( { - 2 - 3} \right) - 3\left( { - 3 - 7} \right) = 5\]
\[\Rightarrow 5\left( { - 5} \right) - 3\left( { - 10} \right) = 5\]
\[\Rightarrow - 25 + 30 = 5\]
\[ \Rightarrow 5 = 5\]
Hence the obtained answer 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.