Question

Solve
\[4(3x + 2) - 5(6x - 1) = 2(x - 8) - 6(7x - 4)\]
A. \[ - \dfrac{3}{2}\]
B. \[ - \dfrac{5}{2}\]
C. \[\dfrac{5}{{22}}\]
D. \[ - \dfrac{5}{{22}}\]

Answer 1

Hint: In the given problem we need to solve this for ‘x’. We can solve this using the transposition method. First we need to expand the brackets on both sides of the equation and then we apply the mathematical operations on like terms and constants. Then finally we separate variables on one side and the constants on the other side of the equation.

Complete step by step answer:
Given, \[4(3x + 2) - 5(6x - 1) = 2(x - 8) - 6(7x - 4)\].
Now expand the brackets we have,
\[12x + 8 - 30x + 5 = 2x - 16 - 42x + 24\]
Now applying the mathematical operations on like terms,
\[13 - 18x = - 40x + 8\]
We transpose ‘13’ which is present in the left hand side of the equation to the right hand side of the equation by subtracting ‘13’ on the right hand side of the equation.
\[ - 18x = - 40x + 8 - 13\]
Similarly we transpose ‘-40x’ to the left hand side of the equation by adding ‘40x’ on the left hand side of the equation.
\[40x - 18x = 8 - 13\]
\[22x = - 5\]
Divide the whole equation by 22,
\[ \Rightarrow x = \dfrac{{ - 5}}{{22}}\].

So, the correct answer is “Option D”.

Note:
While expanding we need to take care of sign change. We know that the product of two negative numbers results in a positive number. The product of negative (Positive) and a positive (negative) number results in a negative number.
 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.