Question

Please someone solve this ​

Answer 1

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Answer 2

Let's solve your equation step-by-step.

$\dfrac{9x+5}{14}+\dfrac{8x-7}{7}=\dfrac{18x+11}{28}+\dfrac{5}{4}$

Step 1: Simplify both sides of the equation.

⇒ $\dfrac{9x+5}{14}+\dfrac{8x-7}{7}=\dfrac{18x+11}{28}+\dfrac{5}{4}$

(Distribute)

⇒ $\dfrac{9}{14}x+ \dfrac{5}{14}+\dfrac{8}{7}x+-1= \dfrac{9}{14}x+\dfrac{11}{28}+ \dfrac{5}{4}$

(Combine Like Terms)

⇒ $(\dfrac{9}{14}x+\dfrac{8}{7}x)+ (\dfrac{5}{14}+-1)= (\dfrac{9}{14}x)+(\dfrac{11}{28}+ \dfrac{5}{4})$

⇒ $\dfrac{25}{14}x+\dfrac{-9}{14}=\dfrac{9}{14}x+\dfrac{23}{14}$

Step 2: Subtract $\bf \frac{9}{14}x$ from both sides.

⇒ $\dfrac{25}{14}x+\dfrac{-9}{14}-\dfrac{9}{14}x=\dfrac{9}{14}x+\dfrac{23}{14}-\dfrac{9}{14}x$

⇒ $\dfrac{8}{7}x+ \dfrac{-9}{14}=\dfrac{23}{14}$

Step 3: Add $\bf \frac{9}{14}$ to both sides.

⇒ $\dfrac{8}{7}x+ \dfrac{-9}{14}+\dfrac{9}{14}=\dfrac{23}{14}+\dfrac{9}{14}$

⇒ $\dfrac{8}{7}x = \dfrac{16}{7}$

Step 4: Multiply both sides by $\bf \frac{7}{8}$.

⇒ $\dfrac{7}{8} \times \dfrac{8}{7}x =\dfrac{7}{8} \times \dfrac{16}{7}$

⇒ $x=2$

Verification if x = 2

⇒ $\dfrac{9x+5}{14}+\dfrac{8x-7}{7}=\dfrac{18x+11}{28}+\dfrac{5}{4}$

⇒ $\dfrac{(9\times 2 )+5}{14}+\dfrac{(8\times 2) -7}{7}=\dfrac{(18\times 2) +11}{28}+\dfrac{5}{4}$

⇒ $\dfrac{18+5}{14}+\dfrac{16 -7}{7}=\dfrac{36 +11}{28}+\dfrac{5}{4}$

⇒ $\dfrac{23}{14}+\dfrac{9}{7}=\dfrac{47}{28}+\dfrac{5}{4}$

⇒ $\dfrac{23}{14}+\dfrac{9\times 2 }{7\times 2 }=\dfrac{47}{28}+\dfrac{5\times 7 }{4\times 7 }$

⇒ $\dfrac{23}{14}+\dfrac{18 }{14 }=\dfrac{47}{28}+\dfrac{35 }{28 }$

⇒ $\dfrac{41}{14}=\dfrac{82}{28}$

⇒ $\dfrac{41}{14}=\dfrac{82\div 2 }{28\div 2 }$

⇒ $\dfrac{41}{14}=\dfrac{41}{14}$

$\sf \bf \therefore x = 2 \ in \ the \ equation \rightarrow \dfrac{9x+5}{14}+\dfrac{8x-7}{7}=\dfrac{18x+11}{28}+\dfrac{5}{4}$