Finite Math Examples

$(5.1 \cdot 10^{5}) x + 7.5 \cdot 10^{4} = 3.9 \cdot 10^{5}$

Step 1

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

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Step 1.1

Subtract $7.5 \cdot 10^{4}$ from both sides of the equation.

$5.1 \cdot 10^{5} x = 3.9 \cdot 10^{5} - 7.5 \cdot 10^{4}$

Step 1.2

Move the decimal point in $- 7.5$ to the left by $1$ place and increase the power of $10^{4}$ by $1$ .

$5.1 \cdot 10^{5} x = 3.9 \cdot 10^{5} - 0.75 \cdot 10^{5}$

Step 1.3

Factor $10^{5}$ out of $3.9 \cdot 10^{5} - 0.75 \cdot 10^{5}$ .

$5.1 \cdot 10^{5} x = (3.9 - 0.75) \cdot 10^{5}$

Step 1.4

Subtract $0.75$ from $3.9$ .

$5.1 \cdot 10^{5} x = 3.15 \cdot 10^{5}$

Step 2

Divide each term in $5.1 \cdot 10^{5} x = 3.15 \cdot 10^{5}$ by $5.1 \cdot 10^{5}$ and simplify.

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Step 2.1

Divide each term in $5.1 \cdot 10^{5} x = 3.15 \cdot 10^{5}$ by $5.1 \cdot 10^{5}$ .

$\frac{5.1 \cdot 10^{5} x}{5.1 \cdot 10^{5}} = \frac{3.15 \cdot 10^{5}}{5.1 \cdot 10^{5}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5.1$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5.1 \cdot 10^{5} x}{5.1 \cdot 10^{5}} = \frac{3.15 \cdot 10^{5}}{5.1 \cdot 10^{5}}$

Step 2.2.1.2

Rewrite the expression.

$\frac{10^{5} x}{10^{5}} = \frac{3.15 \cdot 10^{5}}{5.1 \cdot 10^{5}}$

Step 2.2.2

Cancel the common factor of $10^{5}$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{10^{5} x}{10^{5}} = \frac{3.15 \cdot 10^{5}}{5.1 \cdot 10^{5}}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x = \frac{3.15 \cdot 10^{5}}{5.1 \cdot 10^{5}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide using scientific notation.

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Step 2.3.1.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$x = (\frac{3.15}{5.1}) (\frac{10^{5}}{10^{5}})$

Step 2.3.1.2

Divide $3.15$ by $5.1$ .

$x = 0.61764705 \frac{10^{5}}{10^{5}}$

Step 2.3.1.3

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$x = 0.61764705 \cdot 10^{5 + 5 \cdot - 1}$

Step 2.3.1.4

Multiply $5$ by $- 1$ .

$x = 0.61764705 \cdot 10^{5 - 5}$

Step 2.3.1.5

Subtract $5$ from $5$ .

$x = 0.61764705 \cdot 10^{0}$

Step 2.3.2

Move the decimal point in $0.61764705$ to the right by $1$ place and decrease the power of $10^{0}$ by $1$ .

$x = 6.17647058 \cdot 10^{- 1}$

Step 3

The result can be shown in multiple forms.

Scientific Notation:

$x = 6.17647058 \cdot 10^{- 1}$

Expanded Form:

$x = 0.61764705$