Finite Math Examples

$5 x \div 2 - 4 = 2 x - 7 \div 7$

Step 1

Rewrite the division as a fraction.

$\frac{5 x}{2} - 4 = 2 x - 7 \div 7$

Step 2

Simplify each term.

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Step 2.1

Cancel the common factor of $7$ .

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Step 2.1.1

Cancel the common factor.

$\frac{5 x}{2} - 4 = 2 x - 7 \div 7$

Step 2.1.2

Rewrite the expression.

$\frac{5 x}{2} - 4 = 2 x - 1 \cdot 1$

Step 2.2

Multiply $- 1$ by $1$ .

$\frac{5 x}{2} - 4 = 2 x - 1$

Step 3

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

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Step 3.1

Subtract $2 x$ from both sides of the equation.

$\frac{5 x}{2} - 4 - 2 x = - 1$

Step 3.2

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

$\frac{5 x}{2} - 2 x \cdot \frac{2}{2} - 4 = - 1$

Step 3.3

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

$\frac{5 x}{2} + \frac{- 2 x \cdot 2}{2} - 4 = - 1$

Step 3.4

Combine the numerators over the common denominator.

$\frac{5 x - 2 x \cdot 2}{2} - 4 = - 1$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $5 x - 2 x \cdot 2$ .

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Step 3.5.1.1.1

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - 2 x \cdot 2}{2} - 4 = - 1$

Step 3.5.1.1.2

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

$\frac{x \cdot 5 + x (- 2 \cdot 2)}{2} - 4 = - 1$

Step 3.5.1.1.3

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

$\frac{x (5 - 2 \cdot 2)}{2} - 4 = - 1$

Step 3.5.1.2

Multiply $- 2$ by $2$ .

$\frac{x (5 - 4)}{2} - 4 = - 1$

Step 3.5.1.3

Subtract $4$ from $5$ .

$\frac{x \cdot 1}{2} - 4 = - 1$

Step 3.5.2

Multiply $x$ by $1$ .

$\frac{x}{2} - 4 = - 1$

Step 4

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

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Step 4.1

Add $4$ to both sides of the equation.

$\frac{x}{2} = - 1 + 4$

Step 4.2

Add $- 1$ and $4$ .

$\frac{x}{2} = 3$

Step 5

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 3$

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

Cancel the common factor of $2$ .

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Step 6.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 3$

Step 6.1.1.2

Rewrite the expression.

$x = 2 \cdot 3$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $2$ by $3$ .

$x = 6$