Solve for the variable x

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01-02-2019
Mathematics

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Solve for the variable x

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MisterBrian MisterBrian · Answer 1 · 2021-12-20T15:37:44+01:00

Hello there!

Question:-

[tex](x-2)/3 \: = \: (x+1)/4[/tex]

We need to find the value of x.

Solution:-

[tex]\sf \longmapsto \: \dfrac{x - 2}{3} = \dfrac{x + 2}{4} [/tex]

Firstly, use Cross Multiplication:-

[tex]\sf \longmapsto \: (x - 2)*(4)=(x+1)*(3)[/tex]

On Simplification:-

[tex]\sf \longmapsto \: 4x - 8 = (x + 1)*3[/tex]

[tex]\sf \longmapsto \: 4x - 8 = 3x + 3[/tex]

Subtract 3x from both sides :-

[tex]\sf \longmapsto \: 4x - 8 - 3x=3x+3 - 3x[/tex]

This equation may be rewritten as :-

[tex]\sf \longmapsto4x - 3x - 8 = 3x - 3x + 3[/tex]

On Simplification:-

[tex]\sf \longmapsto \: x - 8 = 0x + 3[/tex]

[tex]\sf \longmapsto \: x - 8 = 3[/tex]

Add 8 to both sides:-

[tex]\sf \longmapsto \: x - 8 + 8 = 3 + 8[/tex]

As (-)and (+) equals to (-),

[tex]\sf \longmapsto \: x - 0 = 11[/tex]

[tex] \: \sf \longmapsto \: x = 11[/tex]

______________________________________

Henceforth, the value of x is :-

[tex] \boxed{\huge\tt x = 11}[/tex]

______________________________________

Please let me know if you have any questions.

~MisterBrian

SalmonWorldTopper SalmonWorldTopper · Answer 2 · 2021-12-21T00:51:18+01:00

Given fractional expression:

[tex]{\sf \longmapsto \dfrac{x-2}{3} = \dfrac{x+1}{4}}[/tex]

Cross multiply the numbers.

[tex]{\sf \longmapsto 4 (x-2) = 3 (x +1)}[/tex]

Multiply the number outside the bracket with the numbers in the bracket.

[tex]{\sf \longmapsto 4x - 8 = 3x +3}[/tex]

Shift all variables on LHS and constants on RHS.

[tex]{\sf \longmapsto 4x - 3x = 3+8}[/tex]

Subtract the values on LHS and Add the values on RHS.

[tex]{\sf \longmapsto 7x = (11)}[/tex]

Shift the number 7 from LHS to RHS.

[tex]{\sf \longmapsto x = \dfrac{11}{7}}[/tex]

[tex]\underline{\boxed{\bf So, \: the \: value \: of \: x \: is \: \dfrac{11}{7}.}}[/tex]

Verification :

[tex]{\sf \longmapsto \dfrac{x-2}{3} = \dfrac{x+1}{4}}[/tex]

Substitute the value of the x.

[tex]{\sf \longmapsto \dfrac{\frac{11}{7}-2}{3}= \dfrac{\frac{11}{7}+1}{4}}[/tex]

[tex]{\sf \longmapsto \dfrac{\frac{11-14}{7}}{3} = \dfrac{\frac{11+7}{7}}{4}}[/tex]

[tex]{\sf \longmapsto \dfrac{\frac{-3}{7}}{3}= \dfrac{\dfrac{18}{7}}{4}}[/tex]

Cancel the number 7 on numerator Of LHS and RHS.

[tex]{\sf \longmapsto \dfrac{-3}{3} = \dfrac{18}{4}}[/tex]

Write the fraction in lowest form by cancellation method.

[tex]{\sf \longmapsto \dfrac{-3}{3} = \dfrac{9}{2}}[/tex]

So,

[tex]{\sf \longmapsto LHS ≠ RHS}[/tex]