Linear Algebra Examples

$2 s + 5 = \frac{7}{9}$

Step 1

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

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Step 1.1

Subtract $5$ from both sides of the equation.

$2 s = \frac{7}{9} - 5$

Step 1.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$2 s = \frac{7}{9} - 5 \cdot \frac{9}{9}$

Step 1.3

Combine $- 5$ and $\frac{9}{9}$ .

$2 s = \frac{7}{9} + \frac{- 5 \cdot 9}{9}$

Step 1.4

Combine the numerators over the common denominator.

$2 s = \frac{7 - 5 \cdot 9}{9}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 5$ by $9$ .

$2 s = \frac{7 - 45}{9}$

Step 1.5.2

Subtract $45$ from $7$ .

$2 s = \frac{- 38}{9}$

Step 1.6

Move the negative in front of the fraction.

$2 s = - \frac{38}{9}$

Step 2

Divide each term in $2 s = - \frac{38}{9}$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 s = - \frac{38}{9}$ by $2$ .

$\frac{2 s}{2} = \frac{- \frac{38}{9}}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 s}{2} = \frac{- \frac{38}{9}}{2}$

Step 2.2.1.2

Divide $s$ by $1$ .

$s = \frac{- \frac{38}{9}}{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$s = - \frac{38}{9} \cdot \frac{1}{2}$

Step 2.3.2

Cancel the common factor of $2$ .

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Step 2.3.2.1

Move the leading negative in $- \frac{38}{9}$ into the numerator.

$s = \frac{- 38}{9} \cdot \frac{1}{2}$

Step 2.3.2.2

Factor $2$ out of $- 38$ .

$s = \frac{2 (- 19)}{9} \cdot \frac{1}{2}$

Step 2.3.2.3

Cancel the common factor.

$s = \frac{2 \cdot - 19}{9} \cdot \frac{1}{2}$

Step 2.3.2.4

Rewrite the expression.

$s = \frac{- 19}{9}$

Step 2.3.3

Move the negative in front of the fraction.

$s = - \frac{19}{9}$

Step 3

The domain is the set of all valid $s$ values.

${s | s = - \frac{19}{9}}$

Step 4