Question

solve for x 4 upon 9 = x-1 upon 2x-1​

Answer 1

$\large\sf\underline{Question\::}$

Solve for x :

• $\sf\:\frac{4}{9}=\frac{x-1}{2x-1}$

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$\large\sf\underline{Answer\::}$

• The required value of x is $\large{\mathfrak\purple{5}}$ .

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$\large\sf\underline{Given\::}$

• $\sf\:\frac{4}{9}=\frac{x-1}{2x-1}$

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$\large\sf\underline{To\:find\::}$

• Value of x

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

$\sf\:\frac{4}{9}=\frac{x-1}{2x-1}$

• Cross multiplying

$\sf\implies\:4(2x-1)=9(x-1)$

• Multiplying the terms and removing brackets

$\sf\implies\:8x-4=9x-9$

• Transposing -4 from LHS to RHS it becomes +4

$\sf\implies\:8x=9x-9+4$

$\sf\implies\:8x=9x-5$

• Transposing +9x from RHS to LHS it becomes -9x

$\sf\implies\:8x-9x=-5$

$\sf\implies\:-1x=-5$

$\sf\implies\:\cancel{-}x=\cancel{-}5$

$\small{\underline{\boxed{\mathrm\red{\implies\:x\:=\:5}}}}$ ★

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$\large\sf\underline{Verifying\::}$

For verifying we will substitute the value of x as 5 in the given equation. After doing so if we get LHS = RHS our answers would be correct.

Let's do and see :

$\sf\:\frac{4}{9}=\frac{x-1}{2x-1}$

• Substituting x as 5

$\sf\implies\:\frac{4}{9}=\frac{5-1}{2(5)-1}$

$\sf\implies\:\frac{4}{9}=\frac{4}{10-1}$

$\sf\implies\:\frac{4}{9}=\frac{4}{9}$

$\sf\implies\:36=36$

$\bf\implies\:LHS=RHS$

$\tt\green{Hence\:Verified}$

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!! Hope it helps !!