Linear Algebra Examples

$- 5 = 25 x - 100$

Step 1

Rewrite the equation as $25 x - 100 = - 5$ .

$25 x - 100 = - 5$

Step 2

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

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Step 2.1

Add $100$ to both sides of the equation.

$25 x = - 5 + 100$

Step 2.2

Add $- 5$ and $100$ .

$25 x = 95$

Step 3

Divide each term in $25 x = 95$ by $25$ and simplify.

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Step 3.1

Divide each term in $25 x = 95$ by $25$ .

$\frac{25 x}{25} = \frac{95}{25}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $25$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{25 x}{25} = \frac{95}{25}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{95}{25}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $95$ and $25$ .

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Step 3.3.1.1

Factor $5$ out of $95$ .

$x = \frac{5 (19)}{25}$

Step 3.3.1.2

Cancel the common factors.

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Step 3.3.1.2.1

Factor $5$ out of $25$ .

$x = \frac{5 \cdot 19}{5 \cdot 5}$

Step 3.3.1.2.2

Cancel the common factor.

$x = \frac{5 \cdot 19}{5 \cdot 5}$

Step 3.3.1.2.3

Rewrite the expression.

$x = \frac{19}{5}$

Step 4

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

${x | x = \frac{19}{5}}$

Step 5