Question

Solve the following linear equation :— 2x + ⅔ = ⅖ — x​

Answer 1

Answer :-

• The value of x is -4/45.

To find :-

• The value of x.

Solution :-

$\longmapsto\sf2x + \dfrac{2}{3} = \dfrac{2}{5} - x$

Transposing x from RHS to LHS, changing it's sign,

$\longmapsto\sf2x + x = \dfrac{2}{5} - \dfrac{2}{3}$

Adding x to 2x,

$\longmapsto\sf3x = \dfrac{2}{5} - \dfrac{2}{3}$

The LCM of 5 and 3 is 15, so subtracting the fractions using their LCM,

$\longmapsto\sf3x = \dfrac{2 \times 3 - 2 \times 5}{15}$

On simplifying,

$\longmapsto\sf3x = \dfrac{6 - 10}{15}$

Subtracting 10 from 6,

$\longmapsto\sf3x = \dfrac{ - 4}{ \: \: 15}$

Transposing 3 from LHS to RHS, changing it's sign,

$\longmapsto\sf x = \dfrac{ - 4}{ \: \: 15} \div 3$

The reciprocal of 3 is 1/3, so we now have to multiply -4/15 with 1/3,

$\longmapsto\sf x = \dfrac{ - 4}{ \: \: 15} \times \dfrac{1}{3}$

Multiplying the fractions,

$\longmapsto \underline{\boxed{\sf x = \dfrac{ - 4}{ \: 45}}}$

Hence :-

• The value of x is -4/45.

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