Question

Solve the linear equation: $\dfrac{{(2x + 3) - (5x - 7)}}{{6x + 11}} = - \dfrac{8}{3}$

Answer 1

Hint: We can use the transposition approach to solve this question. The most common approach of transposition is to execute the identical thing (mathematically) on both sides of the equation in order to bring like terms together and isolate the variable (or the unknown quantity). That is, we group the ‘x' terms on one side of the equation and the constants on the other.

Complete step by step solution:
We have given $\dfrac{{(2x + 3) - (5x - 7)}}{{6x + 11}} = - \dfrac{8}{3}$
 We remove the brackets and simplify the numerator.
$ \Rightarrow \dfrac{{2x + 3 - 5x + 7}}{{6x + 11}} = - \dfrac{8}{3}$
$ \Rightarrow \dfrac{{ - 3x + 10}}{{6x + 11}} = - \dfrac{8}{3}$
 We have cross multiply them for simplification,
$ \Rightarrow 3( - 3x + 10) = - 8(6x + 11)$
$ \Rightarrow - 9x + 30 = - 48x - 88$
We transpose our x to one side and numerical values to other side
$ \Rightarrow 48x - 9x = - 88 - 30$
$ \Rightarrow 39x = - 118$
$ \Rightarrow x = - \dfrac{{118}}{{39}}$
The value of x in $\dfrac{{(2x + 3) - (5x - 7)}}{{6x + 11}} = - \dfrac{8}{3}$ is $ - \dfrac{{118}}{{39}}$ .

Note: We can also check our answer simply by putting the value of x in the $\dfrac{{(2x + 3) - (5x - 7)}}{{6x + 11}} = - \dfrac{8}{3}$ . we get the right value if after putting the value of x in the equation, left hand side is equal to right hand side. The most common mistake we made is putting the wrong sign while removing brackets or while multiplying.