Precalculus Examples

$9 - 2 s = 2 (9 - s t)$

Step 1

Simplify $2 (9 - s t)$ .

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Step 1.1

Rewrite.

$9 - 2 s = 0 + 0 + 2 (9 - s t)$

Step 1.2

Simplify by adding zeros.

$9 - 2 s = 2 (9 - s t)$

Step 1.3

Apply the distributive property.

$9 - 2 s = 2 \cdot 9 + 2 (- s t)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $9$ .

$9 - 2 s = 18 + 2 (- s t)$

Step 1.4.2

Multiply $- 1$ by $2$ .

$9 - 2 s = 18 - 2 s t$

Step 2

Add $2 s t$ to both sides of the equation.

$9 - 2 s + 2 s t = 18$

Step 3

Move all terms not containing $s$ to the right side of the equation.

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Step 3.1

Subtract $9$ from both sides of the equation.

$- 2 s + 2 s t = 18 - 9$

Step 3.2

Subtract $9$ from $18$ .

$- 2 s + 2 s t = 9$

Step 4

Factor $2 s$ out of $- 2 s + 2 s t$ .

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Step 4.1

Factor $2 s$ out of $- 2 s$ .

$2 s (- 1) + 2 s t = 9$

Step 4.2

Factor $2 s$ out of $2 s t$ .

$2 s (- 1) + 2 s (t) = 9$

Step 4.3

Factor $2 s$ out of $2 s (- 1) + 2 s (t)$ .

$2 s (- 1 + t) = 9$

Step 5

Divide each term in $2 s (- 1 + t) = 9$ by $2 (- 1 + t)$ and simplify.

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Step 5.1

Divide each term in $2 s (- 1 + t) = 9$ by $2 (- 1 + t)$ .

$\frac{2 s (- 1 + t)}{2 (- 1 + t)} = \frac{9}{2 (- 1 + t)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 s (- 1 + t)}{2 (- 1 + t)} = \frac{9}{2 (- 1 + t)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{s (- 1 + t)}{- 1 + t} = \frac{9}{2 (- 1 + t)}$

Step 5.2.2

Cancel the common factor of $- 1 + t$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{s (- 1 + t)}{- 1 + t} = \frac{9}{2 (- 1 + t)}$

Step 5.2.2.2

Divide $s$ by $1$ .

$s = \frac{9}{2 (- 1 + t)}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Rewrite $- 1$ as $- 1 (1)$ .

$s = \frac{9}{2 (- 1 (1) + t)}$

Step 5.3.2

Factor $- 1$ out of $t$ .

$s = \frac{9}{2 (- 1 (1) - 1 (- t))}$

Step 5.3.3

Factor $- 1$ out of $- 1 (1) - 1 (- t)$ .

$s = \frac{9}{2 (- 1 (1 - t))}$

Step 5.3.4

Move the negative in front of the fraction.

$s = - \frac{9}{2 (1 - t)}$