Question

Solve
\[7(3x - 1) - 6(2x + 3) = 8(x - 2) + 1\]

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We first expand the brackets in both sides of the equation and we add like terms and constant terms. Then we can solve this using the transposition method. That is, we group the ‘x’ terms on one side and constants on the other side of the equation.

Complete step-by-step answer:
Given, \[7(3x - 1) - 6(2x + 3) = 8(x - 2) + 1\].
Now expanding the brackets we have,
\[21x - 7 - 12x - 18 = 8x - 16 + 1\]
Now grouping like terms and constants in both LHS and RHS.
\[21x - 12x - 18 - 7 = 8x - 16 + 1\]
Adding or subtracting like terms and constants we have,
\[9x - 25 = 8x - 15\]
We transpose ‘-25’ which is present on the left-hand side of the equation to the right-hand side of the equation by adding ‘25’ on the right-hand side of the equation.
\[9x = 8x - 15 + 25\]
We transpose ‘8x’ to the left-hand side of the equation by subtracting 8x on the LHS.
\[9x - 8x = - 15 + 25\]
Thus we have separated variable and the constant terms,
\[ \Rightarrow x = 10\].This is the required answer.

Note: We can check whether the obtained solution is correct or wrong. All we need to do is substituting the value of ‘x’ in the given problem.
\[7(3x - 1) - 6(2x + 3) = 8(x - 2) + 1\]
\[7(3(10) - 1) - 6(2(10) + 3) = 8((10) - 2) + 1\]
\[7(30 - 1) - 6(20 + 3) = 8(10 - 2) + 1\]
\[7(29) - 6(23) = 8(8) + 1\]
\[203 - 138 = 64 + 1\]
Simplifying we have,
\[ \Rightarrow 65 = 65\].
That is LHS=RHS. Hence the obtained is correct.
We need to be careful in simplifying, we need to follow the BODMAS rule. 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.