Identify LCM of Denominators: Identify the least common multiple (LCM) of the denominators in the equation.The denominators are 3 and 21. The LCM of 3 and 21 is 21.
Multiply by LCM: Multiply every term in the equation by the LCM to eliminate the fractions.Multiplying each term by 21 gives us 21(37)+21(21x−1)=21(x+8).
Simplify by Multiplication: Simplify the equation by performing the multiplication.This results in 7×7+(x−1)=21x+21×8.
Further Simplify Equation: Further simplify the equation by carrying out the multiplication.We get 49+x−1=21x+168.
Combine Like Terms: Combine like terms on both sides of the equation.This simplifies to x+48=21x+168.
Subtract to Get x Terms: Subtract x from both sides to get all x terms on one side.This gives us 48=20x+168.
Isolate x Term: Subtract 168 from both sides to isolate the x term.This results in −120=20x.
Divide to Solve for x: Divide both sides by 20 to solve for x.This gives us x=−20120.
Simplify Division: Simplify the division to find the value of x. We find that x=−6.
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