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Solving Linear Equations Using Property of Equality

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Question

What is the value of $x$ for the equation $\frac{5 x - 4}{6} = 4 x + 1 - \frac{3 x + 10}{2}$ ?

A

2

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B

-2

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C

4

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D

5

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Solution

The correct option is A
2

$\frac{(5 x - 4)}{6} = (4 x + 1) - \frac{(3 x + 10)}{2}$
Taking LCM on the right hand side of the equation, we have

$\Rightarrow \frac{(5 x - 4)}{6} = \frac{2 (4 x + 1) - (3 x + 10)}{2}$ [LCM of 1 and 2 = 2]
Cross multiplying, we get
$\Rightarrow (5 x - 4) (2) = 6 [2 (4 x + 1) - (3 x + 10)]$
$\Rightarrow 10 x - 8 = 6 [8 x + 2 - 3 x - 10]$
$\Rightarrow 10 x - 8 = 6 [5 x - 8]$
$\Rightarrow 10 x - 8 = 30 x - 48$
$\Rightarrow 10 x - 30 x = 8 - 48$
$\Rightarrow - 20 x = - 40$
Multiplying both sides by (-1), we get
$\Rightarrow 20 x = 40$
$\Rightarrow x = \frac{40}{20}$
$\Rightarrow x = 2$

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Similar questions

Q. What is the value of x in the equation

2 x + 4 = 10 ?

x

\frac{5 x - 4}{6} = 4 x + 1 - \frac{3 x + 10}{2}

$F i n d t h e v a l u e o f x : \frac{1}{1 + \frac{1}{1 - x}} = 2$

\frac{5 x - 4}{6} = 4 x + 1 - \frac{3 x + 10}{2}

Solve :

$\frac{5 x - 4}{6} = 4 x + 1 - \frac{3 x + 10}{2}$

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