d) (15 x)/(4)=(9)/(4)-(3-x)/(2)

Find Common Denominator: First, we need to find a common denominator to combine the terms on the right side of the equation. The common denominator for 4 and 2 is 4.Rewrite with Common Denominator: Now we rewrite the equation with the common denominator: (15x)/4 = (9/4) - (2*(3-x))/4Simplify Right Side: Simplify the right side of the equation by distributing the 2 into (3-x): (15x)/4 = (9/4) - (6-2x)/4Combine Right Side Terms: Combine the terms on the right side of the equation: (15x)/4 = (9 - 6 + 2x)/4Further Simplify Right Side: Simplify the right side further: (15x)/4 = (3 + 2x)/4Equate Numerators: Now we have an equation with the same denominator on both sides, so we can equate the numerators: 15x = 3 + 2xSubtract and Combine Terms: Subtract 2x from both sides to get all x terms on one side: 15x - 2x = 3Divide to Solve for x: Combine like terms: 13x = 3Divide both sides by 13 to solve for x: x = 3/13

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d) $\frac{15 x}{4}=\frac{9}{4}-\frac{3-x}{2}$

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Algebra 2

Sum of finite series starts from 1

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Q. d)

\frac{15 x}{4}=\frac{9}{4}-\frac{3-x}{2}

Find Common Denominator: First, we need to find a common denominator to combine the terms on the right side of the equation. The common denominator for $4$ and $2$ is $4$ .
Rewrite with Common Denominator: Now we rewrite the equation with the common denominator: $\frac{15x}{4} = \frac{9}{4} - \frac{2(3-x)}{4}$
Simplify Right Side: Simplify the right side of the equation by distributing the $2$ into $(3-x)$ : $\frac{15x}{4} = \frac{9}{4} - \frac{6-2x}{4}$
Combine Right Side Terms: Combine the terms on the right side of the equation: $\newline$ $\frac{15x}{4} = \frac{9 - 6 + 2x}{4}$
Further Simplify Right Side: Simplify the right side further: $(\frac{15x}{4}) = (\frac{3 + 2x}{4})$
Equate Numerators: Now we have an equation with the same denominator on both sides, so we can equate the numerators: $15x = 3 + 2x$
Subtract and Combine Terms: Subtract $2x$ from both sides to get all $x$ terms on one side: $\newline$ $15x - 2x = 3$
Divide to Solve for x: Combine like terms: $13x = 3$
Divide to Solve for x: Combine like terms: $\newline$ $13x = 3$ Divide both sides by $13$ to solve for x: $\newline$ $x = \frac{3}{13}$