x+7-(8x)/(3)=(17)/(6)-(5x)/(2)

Simplify terms: Simplify both sides of the equation by combining like terms. Left side: x + 7 - (8x/3) Right side: (17/6) - (5x/2)Common denominator conversion: Convert all terms to have a common denominator to simplify the equation. Left side: (3x/3) + (21/3) - (8x/3) = (-5x/3) + (21/3) Right side: (17/6) - (15x/6) = (17/6) - (15x/6)Set expressions equal: Set the expressions equal to each other and solve for x. (-5x/3) + (21/3) = (17/6) - (15x/6) Combine x terms: (-5x/3) + (15x/6) = (17/6) - (21/3)Combine x terms: Simplify further by finding a common denominator for x terms and constants. (-10x/6) + (15x/6) = (17/6) - (42/6) (5x/6) = (-25/6) x = (-25/6) / (5/6) x = -5

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$x+7-\frac{8 x}{3}=\frac{17}{6}-\frac{5 x}{2}$

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Algebra 2

Sum of finite series starts from 1

Full solution

x+7-\frac{8 x}{3}=\frac{17}{6}-\frac{5 x}{2}

Simplify terms: Simplify both sides of the equation by combining like terms. $\newline$ Left side: $x + 7 - \left(\frac{8x}{3}\right)$ $\newline$ Right side: $\left(\frac{17}{6}\right) - \left(\frac{5x}{2}\right)$
Common denominator conversion: Convert all terms to have a common denominator to simplify the equation. $\newline$ Left side: $(\frac{3x}{3}) + (\frac{21}{3}) - (\frac{8x}{3}) = (\frac{-5x}{3}) + (\frac{21}{3})$ $\newline$ Right side: $(\frac{17}{6}) - (\frac{15x}{6}) = (\frac{17}{6}) - (\frac{15x}{6})$
Set expressions equal: Set the expressions equal to each other and solve for $x$ . $\frac{-5x}{3} + \frac{21}{3} = \frac{17}{6} - \frac{15x}{6}$ Combine $x$ terms: $\frac{-5x}{3} + \frac{15x}{6} = \frac{17}{6} - \frac{21}{3}$
Combine $x$ terms: Simplify further by finding a common denominator for $x$ terms and constants. $\newline$ $(-10x/6) + (15x/6) = (17/6) - (42/6)$ $\newline$ $(5x/6) = (-25/6)$ $\newline$ $x = (-25/6) / (5/6)$ $\newline$ $x = -5$