Finite Math Examples

$\frac{3}{2} x + 0.9 = \frac{3}{5} + 0.6 x$

Step 1

Combine $\frac{3}{2}$ and $x$ .

$\frac{3 x}{2} + 0.9 = \frac{3}{5} + 0.6 x$

Step 2

Move all terms containing $x$ to the left side of the equation.

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Step 2.1

Subtract $0.6 x$ from both sides of the equation.

$\frac{3 x}{2} + 0.9 - 0.6 x = \frac{3}{5}$

Step 2.2

To write $- 0.6 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 x}{2} - 0.6 x \cdot \frac{2}{2} + 0.9 = \frac{3}{5}$

Step 2.3

Combine $- 0.6 x$ and $\frac{2}{2}$ .

$\frac{3 x}{2} + \frac{- 0.6 x \cdot 2}{2} + 0.9 = \frac{3}{5}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{3 x - 0.6 x \cdot 2}{2} + 0.9 = \frac{3}{5}$

Step 2.5

Simplify each term.

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Step 2.5.1

Simplify the numerator.

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Step 2.5.1.1

Factor $0.6 x$ out of $3 x - 0.6 x \cdot 2$ .

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Step 2.5.1.1.1

Move $x$ .

$\frac{3 x - 0.6 \cdot 2 x}{2} + 0.9 = \frac{3}{5}$

Step 2.5.1.1.2

Factor $0.6 x$ out of $3 x$ .

$\frac{0.6 x (5) - 0.6 \cdot 2 x}{2} + 0.9 = \frac{3}{5}$

Step 2.5.1.1.3

Factor $0.6 x$ out of $- 0.6 \cdot 2 x$ .

$\frac{0.6 x (5) + 0.6 x (- 1 \cdot 2)}{2} + 0.9 = \frac{3}{5}$

Step 2.5.1.1.4

Factor $0.6 x$ out of $0.6 x (5) + 0.6 x (- 1 \cdot 2)$ .

$\frac{0.6 x (5 - 1 \cdot 2)}{2} + 0.9 = \frac{3}{5}$

Step 2.5.1.2

Combine exponents.

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Step 2.5.1.2.1

Multiply $- 1$ by $2$ .

$\frac{0.6 x (5 - 2)}{2} + 0.9 = \frac{3}{5}$

Step 2.5.1.2.2

Multiply $5 - 2$ by $0.6$ .

$\frac{1.8 x}{2} + 0.9 = \frac{3}{5}$

Step 2.5.2

Factor $1.8$ out of $1.8 x$ .

$\frac{1.8 (x)}{2} + 0.9 = \frac{3}{5}$

Step 2.5.3

Factor $2$ out of $2$ .

$\frac{1.8 (x)}{2 (1)} + 0.9 = \frac{3}{5}$

Step 2.5.4

Separate fractions.

$\frac{1.8}{2} \cdot \frac{x}{1} + 0.9 = \frac{3}{5}$

Step 2.5.5

Divide $1.8$ by $2$ .

$0.9 \frac{x}{1} + 0.9 = \frac{3}{5}$

Step 2.5.6

Divide $x$ by $1$ .

$0.9 x + 0.9 = \frac{3}{5}$

Step 3

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

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Step 3.1

Subtract $0.9$ from both sides of the equation.

$0.9 x = \frac{3}{5} - 0.9$

Step 3.2

To write $- 0.9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$0.9 x = \frac{3}{5} - 0.9 \cdot \frac{5}{5}$

Step 3.3

Combine $- 0.9$ and $\frac{5}{5}$ .

$0.9 x = \frac{3}{5} + \frac{- 0.9 \cdot 5}{5}$

Step 3.4

Combine the numerators over the common denominator.

$0.9 x = \frac{3 - 0.9 \cdot 5}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Multiply $- 0.9$ by $5$ .

$0.9 x = \frac{3 - 4.5}{5}$

Step 3.5.2

Subtract $4.5$ from $3$ .

$0.9 x = \frac{- 1.5}{5}$

Step 3.6

Divide $- 1.5$ by $5$ .

$0.9 x = - 0.3$

Step 4

Divide each term in $0.9 x = - 0.3$ by $0.9$ and simplify.

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Step 4.1

Divide each term in $0.9 x = - 0.3$ by $0.9$ .

$\frac{0.9 x}{0.9} = \frac{- 0.3}{0.9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $0.9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{0.9 x}{0.9} = \frac{- 0.3}{0.9}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 0.3}{0.9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 0.3$ by $0.9$ .

$x = - 0.\overline{3}$