Basic Math Examples

$3 (y - \frac{1}{7}) - y = 4 (2 - y)$

Step 1

Simplify $3 (y - \frac{1}{7}) - y$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 y + 3 (- \frac{1}{7}) - y = 4 (2 - y)$

Step 1.1.2

Multiply $3 (- \frac{1}{7})$ .

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Step 1.1.2.1

Multiply $- 1$ by $3$ .

$3 y - 3 (\frac{1}{7}) - y = 4 (2 - y)$

Step 1.1.2.2

Combine $- 3$ and $\frac{1}{7}$ .

$3 y + \frac{- 3}{7} - y = 4 (2 - y)$

Step 1.1.3

Move the negative in front of the fraction.

$3 y - \frac{3}{7} - y = 4 (2 - y)$

Step 1.2

Subtract $y$ from $3 y$ .

$2 y - \frac{3}{7} = 4 (2 - y)$

Step 2

Simplify $4 (2 - y)$ .

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Step 2.1

Apply the distributive property.

$2 y - \frac{3}{7} = 4 \cdot 2 + 4 (- y)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $4$ by $2$ .

$2 y - \frac{3}{7} = 8 + 4 (- y)$

Step 2.2.2

Multiply $- 1$ by $4$ .

$2 y - \frac{3}{7} = 8 - 4 y$

Step 3

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

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Step 3.1

Add $4 y$ to both sides of the equation.

$2 y - \frac{3}{7} + 4 y = 8$

Step 3.2

Add $2 y$ and $4 y$ .

$6 y - \frac{3}{7} = 8$

Step 4

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

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Step 4.1

Add $\frac{3}{7}$ to both sides of the equation.

$6 y = 8 + \frac{3}{7}$

Step 4.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$6 y = 8 \cdot \frac{7}{7} + \frac{3}{7}$

Step 4.3

Combine $8$ and $\frac{7}{7}$ .

$6 y = \frac{8 \cdot 7}{7} + \frac{3}{7}$

Step 4.4

Combine the numerators over the common denominator.

$6 y = \frac{8 \cdot 7 + 3}{7}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $8$ by $7$ .

$6 y = \frac{56 + 3}{7}$

Step 4.5.2

Add $56$ and $3$ .

$6 y = \frac{59}{7}$

Step 5

Divide each term in $6 y = \frac{59}{7}$ by $6$ and simplify.

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Step 5.1

Divide each term in $6 y = \frac{59}{7}$ by $6$ .

$\frac{6 y}{6} = \frac{\frac{59}{7}}{6}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $6$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{\frac{59}{7}}{6}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{\frac{59}{7}}{6}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{59}{7} \cdot \frac{1}{6}$

Step 5.3.2

Multiply $\frac{59}{7} \cdot \frac{1}{6}$ .

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Step 5.3.2.1

Multiply $\frac{59}{7}$ by $\frac{1}{6}$ .

$y = \frac{59}{7 \cdot 6}$

Step 5.3.2.2

Multiply $7$ by $6$ .

$y = \frac{59}{42}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{59}{42}$

Decimal Form:

$y = 1.40476190 \dots$

Mixed Number Form:

$y = 1 \frac{17}{42}$