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Solve the expression and find the value of x.
[tex] \frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 [/tex]
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Sagot :

SalmonWorldTopper

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\sf \dfrac{x + 1}{10} - \dfrac{3(x - 1)}{5} = 2[/tex]

[tex]\sf\longmapsto \dfrac{x + 1}{10} - \dfrac{3x - 3}{5} = 2[/tex]

[tex]\sf\longmapsto \dfrac{(x + 1) - 2(3x - 3)}{10} = 2[/tex]

[tex]\sf\longmapsto \dfrac{x + 1 - (6x - 6)}{10} = 2[/tex]

[tex]\sf\longmapsto \dfrac{x + 1 - 6x + 6}{10} = 2[/tex]

[tex]\sf\longmapsto \dfrac{ - 5x + 7}{10} = 2[/tex]

[tex]\sf\longmapsto - 5x + 7 = 20[/tex]

[tex]\sf\longmapsto - 5x = 20 - 7[/tex]

[tex]\sf\longmapsto - 5x = 13[/tex]

[tex]\sf\therefore x = - \dfrac{13}{5} [/tex]

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

ᴜᴋɪʏᴏ

[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]

[tex]\frac{x + 1}{10} - \frac{3(x - 1)}{5} = 2 \\ [/tex]

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

[tex]\frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = 2 \\ \frac { x + 1 } { 10 } - \frac { 3 ( x - 1 ) } { 5 } = \frac{2}{1} [/tex]

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.

[tex]\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} [/tex]

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

[tex]x + 1 - (6x - 6) = 20 \\ [/tex]

Now, simplify it.

[tex]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}}[/tex]

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