Question

Solve the equations
x+7 /x+2 =3/4​

Answer 1

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \longmapsto \dfrac{x}{7} + \dfrac{x}{2} = \dfrac{3}{4}$

How to solve :

step 1:First step is to take LCM of the given term

Step2:Now ,convert into a single fraction form .

Step3:After cross multiply to both sides.

Step4:Make variable's terms one side and constant term on the other.

Step4:Shifts all constant value which are along with Variable to constant side and let the variable single and hence evaluate it to find the variable's value.

LCM of 7 and 2 is 14

$\sf \longmapsto \dfrac{2x + 7x}{14} = \dfrac{3}{4}$

$\sf \longmapsto \dfrac{9x}{14} = \dfrac{3}{4}$

Cross multiply to both sides:

$\sf \longmapsto9x \times 4 = 14 \times 3$

$\sf \longmapsto36x = 42$

$\sf \longmapsto \bold{ x = \dfrac{42}{36} = \dfrac{7}{6}}$

Check:

$\sf \longmapsto \dfrac{9x}{14} = \dfrac{3}{4}$

Taking LHS

$\sf \longmapsto \dfrac{9 \times \dfrac{7}{6} }{14} = \dfrac{3 \times \dfrac{7}{2} }{14} = \dfrac{ \dfrac{21}{2} }{14}$

$\sf \longmapsto \dfrac{21}{28} = \dfrac{3}{4}$

Hence,LHS = RHS(Verified)

Answer 2

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

• $\sf\large\:\frac{x+7}{x+2}=\frac{3}{4}$

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

• Value of x

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

$\sf\large\:\frac{x+7}{x+2}=\frac{3}{4}$

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• Cross multiplying

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$\sf\implies\:4(x+7)=3(x+2)$

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• Multiplying the terms

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$\sf\implies\:4x+28=3x+6$

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• Transposing 3x to other side

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$\sf\implies\:4x-3x+28=6$

$\sf\implies\:x+28=6$

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• Transposing 28 to the other side

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$\sf\implies\:x=6-28$

$\large{\mathfrak\red{\implies\:x\:=\:-22}}$

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

$\sf\:\frac{x+7}{x+2}=\frac{3}{4}$

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• Let's substitute x as (-22)

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$\sf\implies\:\frac{-22+7}{-22+2}=\frac{3}{4}$

$\sf\implies\:\frac{\cancel{-}15}{\cancel{-}20}=\frac{3}{4}$

$\sf\implies\:\cancel{\frac{15}{20}}=\frac{3}{4}$

$\sf\implies\:\frac{3}{4}=\frac{3}{4}$

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$\dag\:\underline{\sf Hence\:Verified\:}$

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Required value of x is $\large\fbox\purple{-22}$ .

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!! Hope it helps !!