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Solve for x. (7)/(3)+(x-1)/(21)=x+8 Answer:

Solve for x \mathrm{x} .\newline73+x−121=x+8 \frac{7}{3}+\frac{x-1}{21}=x+8 \newlineAnswer:

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Full solution

Q. Solve for x \mathrm{x} .\newline73+x−121=x+8 \frac{7}{3}+\frac{x-1}{21}=x+8 \newlineAnswer:
  1. Identify LCM of Denominators: Identify the least common multiple (LCM) of the denominators in the equation.\newlineThe denominators are 33 and 2121. The LCM of 33 and 2121 is 2121.
  2. Multiply by LCM: Multiply every term in the equation by the LCM to eliminate the fractions.\newlineMultiplying each term by 2121 gives us 21(73)+21(x−121)=21(x+8)21\left(\frac{7}{3}\right) + 21\left(\frac{x-1}{21}\right) = 21\left(x+8\right).
  3. Simplify by Multiplication: Simplify the equation by performing the multiplication.\newlineThis results in 7×7+(x−1)=21x+21×87\times7 + (x-1) = 21x + 21\times8.
  4. Further Simplify Equation: Further simplify the equation by carrying out the multiplication.\newlineWe get 49+x−1=21x+16849 + x - 1 = 21x + 168.
  5. Combine Like Terms: Combine like terms on both sides of the equation.\newlineThis simplifies to x+48=21x+168x + 48 = 21x + 168.
  6. Subtract to Get xx Terms: Subtract xx from both sides to get all xx terms on one side.\newlineThis gives us 48=20x+16848 = 20x + 168.
  7. Isolate xx Term: Subtract 168168 from both sides to isolate the xx term.\newlineThis results in −120=20x-120 = 20x.
  8. Divide to Solve for xx: Divide both sides by 2020 to solve for xx.\newlineThis gives us x=−12020x = -\frac{120}{20}.
  9. Simplify Division: Simplify the division to find the value of xx. We find that x=−6x = -6.

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