Finite Math Examples

$\frac{- 2 x}{3} + 50 = \frac{- 16 x}{19} + \frac{1050}{19}$

Step 1

Move the negative in front of the fraction.

$- \frac{2 x}{3} + 50 = \frac{- 16 x}{19} + \frac{1050}{19}$

Step 2

Move the negative in front of the fraction.

$- \frac{2 x}{3} + 50 = - \frac{16 x}{19} + \frac{1050}{19}$

Step 3

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

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Step 3.1

Add $\frac{16 x}{19}$ to both sides of the equation.

$- \frac{2 x}{3} + 50 + \frac{16 x}{19} = \frac{1050}{19}$

Step 3.2

To write $- \frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$- \frac{2 x}{3} \cdot \frac{19}{19} + \frac{16 x}{19} + 50 = \frac{1050}{19}$

Step 3.3

To write $\frac{16 x}{19}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{2 x}{3} \cdot \frac{19}{19} + \frac{16 x}{19} \cdot \frac{3}{3} + 50 = \frac{1050}{19}$

Step 3.4

Write each expression with a common denominator of $57$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{2 x}{3}$ by $\frac{19}{19}$ .

$- \frac{2 x \cdot 19}{3 \cdot 19} + \frac{16 x}{19} \cdot \frac{3}{3} + 50 = \frac{1050}{19}$

Step 3.4.2

Multiply $3$ by $19$ .

$- \frac{2 x \cdot 19}{57} + \frac{16 x}{19} \cdot \frac{3}{3} + 50 = \frac{1050}{19}$

Step 3.4.3

Multiply $\frac{16 x}{19}$ by $\frac{3}{3}$ .

$- \frac{2 x \cdot 19}{57} + \frac{16 x \cdot 3}{19 \cdot 3} + 50 = \frac{1050}{19}$

Step 3.4.4

Multiply $19$ by $3$ .

$- \frac{2 x \cdot 19}{57} + \frac{16 x \cdot 3}{57} + 50 = \frac{1050}{19}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{- 2 x \cdot 19 + 16 x \cdot 3}{57} + 50 = \frac{1050}{19}$

Step 3.6

Simplify the numerator.

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Step 3.6.1

Factor $2 x$ out of $- 2 x \cdot 19 + 16 x \cdot 3$ .

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Step 3.6.1.1

Factor $2 x$ out of $- 2 x \cdot 19$ .

$\frac{2 x (- 1 \cdot 19) + 16 x \cdot 3}{57} + 50 = \frac{1050}{19}$

Step 3.6.1.2

Factor $2 x$ out of $16 x \cdot 3$ .

$\frac{2 x (- 1 \cdot 19) + 2 x (8 \cdot 3)}{57} + 50 = \frac{1050}{19}$

Step 3.6.1.3

Factor $2 x$ out of $2 x (- 1 \cdot 19) + 2 x (8 \cdot 3)$ .

$\frac{2 x (- 1 \cdot 19 + 8 \cdot 3)}{57} + 50 = \frac{1050}{19}$

Step 3.6.2

Combine exponents.

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Step 3.6.2.1

Multiply $- 1$ by $19$ .

$\frac{2 x (- 19 + 8 \cdot 3)}{57} + 50 = \frac{1050}{19}$

Step 3.6.2.2

Multiply $8$ by $3$ .

$\frac{2 x (- 19 + 24)}{57} + 50 = \frac{1050}{19}$

Step 3.6.3

Add $- 19$ and $24$ .

$\frac{2 x \cdot 5}{57} + 50 = \frac{1050}{19}$

Step 3.6.4

Multiply $5$ by $2$ .

$\frac{10 x}{57} + 50 = \frac{1050}{19}$

Step 4

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

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Step 4.1

Subtract $50$ from both sides of the equation.

$\frac{10 x}{57} = \frac{1050}{19} - 50$

Step 4.2

To write $- 50$ as a fraction with a common denominator, multiply by $\frac{19}{19}$ .

$\frac{10 x}{57} = \frac{1050}{19} - 50 \cdot \frac{19}{19}$

Step 4.3

Combine $- 50$ and $\frac{19}{19}$ .

$\frac{10 x}{57} = \frac{1050}{19} + \frac{- 50 \cdot 19}{19}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{10 x}{57} = \frac{1050 - 50 \cdot 19}{19}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 50$ by $19$ .

$\frac{10 x}{57} = \frac{1050 - 950}{19}$

Step 4.5.2

Subtract $950$ from $1050$ .

$\frac{10 x}{57} = \frac{100}{19}$

Step 5

Multiply both sides of the equation by $\frac{57}{10}$ .

$\frac{57}{10} \cdot \frac{10 x}{57} = \frac{57}{10} \cdot \frac{100}{19}$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{57}{10} \cdot \frac{10 x}{57}$ .

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Step 6.1.1.1

Cancel the common factor of $57$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{57}{10} \cdot \frac{10 x}{57} = \frac{57}{10} \cdot \frac{100}{19}$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{10} (10 x) = \frac{57}{10} \cdot \frac{100}{19}$

Step 6.1.1.2

Cancel the common factor of $10$ .

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Step 6.1.1.2.1

Factor $10$ out of $10 x$ .

$\frac{1}{10} (10 (x)) = \frac{57}{10} \cdot \frac{100}{19}$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{10} (10 x) = \frac{57}{10} \cdot \frac{100}{19}$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{57}{10} \cdot \frac{100}{19}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{57}{10} \cdot \frac{100}{19}$ .

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Step 6.2.1.1

Cancel the common factor of $19$ .

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Step 6.2.1.1.1

Factor $19$ out of $57$ .

$x = \frac{19 (3)}{10} \cdot \frac{100}{19}$

Step 6.2.1.1.2

Cancel the common factor.

$x = \frac{19 \cdot 3}{10} \cdot \frac{100}{19}$

Step 6.2.1.1.3

Rewrite the expression.

$x = \frac{3}{10} \cdot 100$

Step 6.2.1.2

Cancel the common factor of $10$ .

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Step 6.2.1.2.1

Factor $10$ out of $100$ .

$x = \frac{3}{10} \cdot (10 (10))$

Step 6.2.1.2.2

Cancel the common factor.

$x = \frac{3}{10} \cdot (10 \cdot 10)$

Step 6.2.1.2.3

Rewrite the expression.

$x = 3 \cdot 10$

Step 6.2.1.3

Multiply $3$ by $10$ .

$x = 30$