Question

solve fast pls i am mark you​

Answer 1

Answer:

$\bold{ x = - \frac{5}{6} }$

Step-by-step explanation:

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⠀⠀⠀⠀■ Question

$\large \sf{ \frac{4x + 9}{3x + 11} = \frac{4x + 3}{3x + 2} }$

Solve for x.

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⠀⠀⠀⠀□ Solution

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• We will cross multiply the above equation

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$\sf (4x + 9)(3x + 2) = (4x + 3)(3x + 11) \\ \\ \sf 4x(3x + 2) + 9(3x + 2) = 4x(3x + 11) + 3(3x + 11) \\ \\ \sf 12 {x}^{2} + 8x + 27x + 18 = 12 {x}^{2} + 44x + 9x + 33 \\ \\ \sf 12 {x}^{2} + 35x + 18 = 12 {x}^{2} + 53x + 33$

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• Now we will take the values of RHS(right hand side) to LHS(left hand side) of the equation. During this, the values of RHS will get opposite sign while going to LHS.

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$\sf 0 = 12 {x}^{2} + 53x + 33 - 12 {x}^{2} - 35x - 18 \\ \\ \sf 0 = 18x + 15$

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• Taking 15 to LHS

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$\sf - 15 = 18x$

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• Dividing both RHS and LHS of the equation by 18

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$\large{ \sf \frac{ - \cancel{15} \tiny {5}}{ \cancel {18} \tiny6 } = x} \\ \\ \boxed{ x = - \frac{5}{6} }$

Answer 2

Answer:

$\textsf{ x=-\dfrac{5}{6} }$

Step-by-step explanation:

Given: $\textsf{ \dfrac{4x+9}{3x+11}=\dfrac{4x+3}{3x+2} }$

1. Cross-multiply

(4x + 9)(3x + 2) = (4x + 3)(3x + 11)

2. Distribute

⟶ (4x + 9)(3x + 2) = (4x + 3)(3x + 11)

⟶ 4x(3x) + 4x(2) + 9(3x) + 9(2) = 4x(3x) + 4x(11) + 3(3x) + 3(11)

⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33

3. Combine like terms

⟶ 12x² + 8x + 27x + 18 = 12x² + 44x + 9x + 33

⟶ 12x² + 35x + 18 = 12x² + 53x + 33

4. Subtract 12x² from both sides

⟶ 12x² - 12x² + 35x + 18 = 12x² - 12x² + 53x +33

⟶ 35x + 18 = 53x + 33

5. Subtract 35x from both sides

⟶ 35x - 35x + 18 = 53x - 35x + 33

⟶ 18 = 18x + 33

6. Subtract 33 from both sides

⟶ 18 = 18x + 33

⟶ 18 - 33 = 18x + 33 - 33

⟶ -15 = 18x

7. Divide both sides by 18 to isolate the variable

$\longrightarrow\textsf{ \dfrac{-15}{18}=\dfrac{18x}{18} }\\\\\\\longrightarrow\textsf{ \dfrac{-15}{18}=x }$

8. Reduce

$\longrightarrow\textsf{ \dfrac{-15\div 3}{18\div 3}=x }\\\\\\\longrightarrow\textsf{ -\dfrac{5}{6}=x }$