Question

Solve the expression and find the value of x.

Answer 1

$\large\underline{\sf{Solution-}}$

$\sf \dfrac{x + 1}{10} - \dfrac{3(x - 1)}{5} = 2$

$\sf\longmapsto \dfrac{x + 1}{10} - \dfrac{3x - 3}{5} = 2$

$\sf\longmapsto \dfrac{(x + 1) - 2(3x - 3)}{10} = 2$

$\sf\longmapsto \dfrac{x + 1 - (6x - 6)}{10} = 2$

$\sf\longmapsto \dfrac{x + 1 - 6x + 6}{10} = 2$

$\sf\longmapsto \dfrac{ - 5x + 7}{10} = 2$

$\sf\longmapsto - 5x + 7 = 20$

$\sf\longmapsto - 5x = 20 - 7$

$\sf\longmapsto - 5x = 13$

$\sf\therefore x = - \dfrac{13}{5}$

Hence, the value of x will be -13/5 respectively.

Answer 2

$\huge \boxed{\mathfrak{Question} \downarrow}$

$\frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2$

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = 2 \\ \frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1}$

Take a look at the denominators. The denominators are 10, 5 & 1. Their LCM is 10. So, multiply the fractions on both the sides of the equation by 10.

$\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} \\ \frac{x + 1}{10} \times \frac{1}{1} - \frac{3x - 3}{5} \times \frac{2}{2} = \frac{2}{1} \times \frac{10}{10} \\ \frac{x + 1}{10} - \frac{6x - 6}{10} = \frac{20}{10}$

Now cancel the denominators (as they have the same value) & take the numerators.

$x + 1 - (6x - 6) = 20$

Now, simplify it.

$x + 1 - (6x - 6) = 20 \\ x + 1 - 6x + 6 = 20 \\ x - 6x + 1 + 6 = 20 \\ - 5x + 7 = 20 \\ - 5x = 13 \\ x = -\frac{13}{5} \\ \boxed{ \boxed{ \bf x = - \frac{13}{5} =\: - 2 \frac{3}{5} = - 2.6}}$

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