Finite Math Examples

$7 y - 7 = \frac{3}{7} \cdot (x + 3)$

Step 1

Simplify $\frac{3}{7} \cdot (x + 3)$ .

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Step 1.1

Rewrite.

$7 y - 7 = 0 + 0 + \frac{3}{7} \cdot (x + 3)$

Step 1.2

Simplify by adding zeros.

$7 y - 7 = \frac{3}{7} \cdot (x + 3)$

Step 1.3

Apply the distributive property.

$7 y - 7 = \frac{3}{7} x + \frac{3}{7} \cdot 3$

Step 1.4

Combine $\frac{3}{7}$ and $x$ .

$7 y - 7 = \frac{3 x}{7} + \frac{3}{7} \cdot 3$

Step 1.5

Multiply $\frac{3}{7} \cdot 3$ .

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Step 1.5.1

Combine $\frac{3}{7}$ and $3$ .

$7 y - 7 = \frac{3 x}{7} + \frac{3 \cdot 3}{7}$

Step 1.5.2

Multiply $3$ by $3$ .

$7 y - 7 = \frac{3 x}{7} + \frac{9}{7}$

Step 2

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

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Step 2.1

Add $7$ to both sides of the equation.

$7 y = \frac{3 x}{7} + \frac{9}{7} + 7$

Step 2.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$7 y = \frac{3 x}{7} + \frac{9}{7} + 7 \cdot \frac{7}{7}$

Step 2.3

Combine $7$ and $\frac{7}{7}$ .

$7 y = \frac{3 x}{7} + \frac{9}{7} + \frac{7 \cdot 7}{7}$

Step 2.4

Combine the numerators over the common denominator.

$7 y = \frac{3 x}{7} + \frac{9 + 7 \cdot 7}{7}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $7$ by $7$ .

$7 y = \frac{3 x}{7} + \frac{9 + 49}{7}$

Step 2.5.2

Add $9$ and $49$ .

$7 y = \frac{3 x}{7} + \frac{58}{7}$

Step 3

Divide each term in $7 y = \frac{3 x}{7} + \frac{58}{7}$ by $7$ and simplify.

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Step 3.1

Divide each term in $7 y = \frac{3 x}{7} + \frac{58}{7}$ by $7$ .

$\frac{7 y}{7} = \frac{\frac{3 x}{7}}{7} + \frac{\frac{58}{7}}{7}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $7$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{\frac{3 x}{7}}{7} + \frac{\frac{58}{7}}{7}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{3 x}{7}}{7} + \frac{\frac{58}{7}}{7}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{3 x}{7} \cdot \frac{1}{7} + \frac{\frac{58}{7}}{7}$

Step 3.3.1.2

Multiply $\frac{3 x}{7} \cdot \frac{1}{7}$ .

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Step 3.3.1.2.1

Multiply $\frac{3 x}{7}$ by $\frac{1}{7}$ .

$y = \frac{3 x}{7 \cdot 7} + \frac{\frac{58}{7}}{7}$

Step 3.3.1.2.2

Multiply $7$ by $7$ .

$y = \frac{3 x}{49} + \frac{\frac{58}{7}}{7}$

Step 3.3.1.3

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{3 x}{49} + \frac{58}{7} \cdot \frac{1}{7}$

Step 3.3.1.4

Multiply $\frac{58}{7} \cdot \frac{1}{7}$ .

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Step 3.3.1.4.1

Multiply $\frac{58}{7}$ by $\frac{1}{7}$ .

$y = \frac{3 x}{49} + \frac{58}{7 \cdot 7}$

Step 3.3.1.4.2

Multiply $7$ by $7$ .

$y = \frac{3 x}{49} + \frac{58}{49}$