Evaluate: sum_(n=3)^(5)(nx-3) Answer:

Understand summation notation: Understand the summation notation. The expression sum_(n=3)^(5)(nx-3) means we need to evaluate (nx-3) for each integer value of n from 3 to 5 and then sum the results.Evaluate for n=3: Evaluate the expression for n=3. Substitute n=3 into the expression (nx-3) to get (3x-3).Evaluate for n=4: Evaluate the expression for n=4. Substitute n=4 into the expression (nx-3) to get (4x-3).Evaluate for n=5: Evaluate the expression for n=5. Substitute n=5 into the expression (nx-3) to get (5x-3).Add results from steps: Add the results from steps 2, 3, and 4. Sum the expressions: (3x-3) + (4x-3) + (5x-3).Combine like terms: Combine like terms. Add the coefficients of x and the constant terms separately: (3x + 4x + 5x) - (3 + 3 + 3).Perform addition: Perform the addition. Calculate the sum of the coefficients of x: 3x + 4x + 5x = 12x. Calculate the sum of the constants: -3 - 3 - 3 = -9.Write final expression: Write the final expression. Combine the results from step 7 to get the final expression: 12x - 9.

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Algebra 2

Evaluate rational expressions II

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Q. Evaluate:

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\sum_{n=3}^{5}(n x-3)

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Answer:

Understand summation notation: Understand the summation notation. The expression $\sum_{n=3}^{5}(nx-3)$ means we need to evaluate $(nx-3)$ for each integer value of $n$ from $3$ to $5$ and then sum the results.
Evaluate for $n=3$ : Evaluate the expression for $n=3$ . Substitute $n=3$ into the expression $(nx-3)$ to get $(3x-3)$ .
Evaluate for $n=4$ : Evaluate the expression for $n=4$ . $\newline$ Substitute $n=4$ into the expression $(nx-3)$ to get $(4x-3)$ .
Evaluate for $n=5$ : Evaluate the expression for $n=5$ . Substitute $n=5$ into the expression $(nx-3)$ to get $(5x-3)$ .
Add results from steps: Add the results from steps $2$ , $3$ , and $4$ . Sum the expressions: $(3x-3) + (4x-3) + (5x-3)$ .
Combine like terms: Combine like terms. $\newline$ Add the coefficients of $x$ and the constant terms separately: $(3x + 4x + 5x) - (3 + 3 + 3)$ .
Perform addition: Perform the addition. $\newline$ Calculate the sum of the coefficients of $x$ : $3x + 4x + 5x = 12x$ . $\newline$ Calculate the sum of the constants: $-3 - 3 - 3 = -9$ .
Write final expression: Write the final expression. $\newline$ Combine the results from step $7$ to get the final expression: $12x - 9$ .