Precalculus Examples

$4 + \sum_{k = 2}^{5} 3 (k - x)$

Step 1

Evaluate $\sum_{k = 2}^{5} 3 (k - x)$ .

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Step 1.1

Simplify the summation.

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Step 1.1.1

Apply the distributive property.

$3 k + 3 (- x)$

Step 1.1.2

Multiply $- 1$ by $3$ .

$3 k - 3 x$

Step 1.1.3

Rewrite the summation.

$\sum_{k = 2}^{5} 3 k - 3 x$

Step 1.2

Expand the series for each value of $k$ .

$3 \cdot 2 - 3 x + 3 \cdot 3 - 3 x + 3 \cdot 4 - 3 x + 3 \cdot 5 - 3 x$

Step 2

Substitute the values back and simplify $4 + 3 \cdot 2 - 3 x + 3 \cdot 3 - 3 x + 3 \cdot 4 - 3 x + 3 \cdot 5 - 3 x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $3$ by $2$ .

$4 + 6 - 3 x + 3 \cdot 3 - 3 x + 3 \cdot 4 - 3 x + 3 \cdot 5 - 3 x$

Step 2.1.2

Multiply $3$ by $3$ .

$4 + 6 - 3 x + 9 - 3 x + 3 \cdot 4 - 3 x + 3 \cdot 5 - 3 x$

Step 2.1.3

Multiply $3$ by $4$ .

$4 + 6 - 3 x + 9 - 3 x + 12 - 3 x + 3 \cdot 5 - 3 x$

Step 2.1.4

Multiply $3$ by $5$ .

$4 + 6 - 3 x + 9 - 3 x + 12 - 3 x + 15 - 3 x$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $4$ and $6$ .

$10 - 3 x + 9 - 3 x + 12 - 3 x + 15 - 3 x$

Step 2.2.2

Add $10$ and $9$ .

$- 3 x + 19 - 3 x + 12 - 3 x + 15 - 3 x$

Step 2.2.3

Subtract $3 x$ from $- 3 x$ .

$- 6 x + 19 + 12 - 3 x + 15 - 3 x$

Step 2.2.4

Subtract $3 x$ from $- 6 x$ .

$- 9 x + 19 + 12 + 15 - 3 x$

Step 2.2.5

Subtract $3 x$ from $- 9 x$ .

$- 12 x + 19 + 12 + 15$

Step 2.2.6

Simplify by adding numbers.

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Step 2.2.6.1

Add $19$ and $12$ .

$- 12 x + 31 + 15$

Step 2.2.6.2

Add $31$ and $15$ .

$- 12 x + 46$