Basic Math Examples

$\frac{3}{7} y - \frac{12}{5} = \frac{5 y + 1}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{3}{7} y - \frac{12}{5}) \cdot 2 = \frac{5 y + 1}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{3}{7} y - \frac{12}{5}) \cdot 2$ .

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Step 2.1.1.1

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

$(\frac{3 y}{7} - \frac{12}{5}) \cdot 2 = \frac{5 y + 1}{2} \cdot 2$

Step 2.1.1.2

Apply the distributive property.

$\frac{3 y}{7} \cdot 2 - \frac{12}{5} \cdot 2 = \frac{5 y + 1}{2} \cdot 2$

Step 2.1.1.3

Multiply $\frac{3 y}{7} \cdot 2$ .

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Step 2.1.1.3.1

Combine $\frac{3 y}{7}$ and $2$ .

$\frac{3 y \cdot 2}{7} - \frac{12}{5} \cdot 2 = \frac{5 y + 1}{2} \cdot 2$

Step 2.1.1.3.2

Multiply $2$ by $3$ .

$\frac{6 y}{7} - \frac{12}{5} \cdot 2 = \frac{5 y + 1}{2} \cdot 2$

Step 2.1.1.4

Multiply $- \frac{12}{5} \cdot 2$ .

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Step 2.1.1.4.1

Multiply $2$ by $- 1$ .

$\frac{6 y}{7} - 2 (\frac{12}{5}) = \frac{5 y + 1}{2} \cdot 2$

Step 2.1.1.4.2

Combine $- 2$ and $\frac{12}{5}$ .

$\frac{6 y}{7} + \frac{- 2 \cdot 12}{5} = \frac{5 y + 1}{2} \cdot 2$

Step 2.1.1.4.3

Multiply $- 2$ by $12$ .

$\frac{6 y}{7} + \frac{- 24}{5} = \frac{5 y + 1}{2} \cdot 2$

Step 2.1.1.5

Move the negative in front of the fraction.

$\frac{6 y}{7} - \frac{24}{5} = \frac{5 y + 1}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 y}{7} - \frac{24}{5} = \frac{5 y + 1}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$\frac{6 y}{7} - \frac{24}{5} = 5 y + 1$

Step 3

Solve for $y$ .

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Step 3.1

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

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Step 3.1.1

Subtract $5 y$ from both sides of the equation.

$\frac{6 y}{7} - \frac{24}{5} - 5 y = 1$

Step 3.1.2

To write $- 5 y$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{6 y}{7} - 5 y \cdot \frac{7}{7} - \frac{24}{5} = 1$

Step 3.1.3

Combine $- 5 y$ and $\frac{7}{7}$ .

$\frac{6 y}{7} + \frac{- 5 y \cdot 7}{7} - \frac{24}{5} = 1$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{6 y - 5 y \cdot 7}{7} - \frac{24}{5} = 1$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $y$ out of $6 y - 5 y \cdot 7$ .

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Step 3.1.5.1.1.1

Factor $y$ out of $6 y$ .

$\frac{y \cdot 6 - 5 y \cdot 7}{7} - \frac{24}{5} = 1$

Step 3.1.5.1.1.2

Factor $y$ out of $- 5 y \cdot 7$ .

$\frac{y \cdot 6 + y (- 5 \cdot 7)}{7} - \frac{24}{5} = 1$

Step 3.1.5.1.1.3

Factor $y$ out of $y \cdot 6 + y (- 5 \cdot 7)$ .

$\frac{y (6 - 5 \cdot 7)}{7} - \frac{24}{5} = 1$

Step 3.1.5.1.2

Multiply $- 5$ by $7$ .

$\frac{y (6 - 35)}{7} - \frac{24}{5} = 1$

Step 3.1.5.1.3

Subtract $35$ from $6$ .

$\frac{y \cdot - 29}{7} - \frac{24}{5} = 1$

Step 3.1.5.2

Move $- 29$ to the left of $y$ .

$\frac{- 29 \cdot y}{7} - \frac{24}{5} = 1$

Step 3.1.5.3

Move the negative in front of the fraction.

$- \frac{29 y}{7} - \frac{24}{5} = 1$

Step 3.2

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

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Step 3.2.1

Add $\frac{24}{5}$ to both sides of the equation.

$- \frac{29 y}{7} = 1 + \frac{24}{5}$

Step 3.2.2

Write $1$ as a fraction with a common denominator.

$- \frac{29 y}{7} = \frac{5}{5} + \frac{24}{5}$

Step 3.2.3

Combine the numerators over the common denominator.

$- \frac{29 y}{7} = \frac{5 + 24}{5}$

Step 3.2.4

Add $5$ and $24$ .

$- \frac{29 y}{7} = \frac{29}{5}$

Step 3.3

Multiply both sides of the equation by $- \frac{7}{29}$ .

$- \frac{7}{29} (- \frac{29 y}{7}) = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Simplify $- \frac{7}{29} (- \frac{29 y}{7})$ .

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Step 3.4.1.1.1

Cancel the common factor of $7$ .

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Step 3.4.1.1.1.1

Move the leading negative in $- \frac{7}{29}$ into the numerator.

$\frac{- 7}{29} (- \frac{29 y}{7}) = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.1.2

Move the leading negative in $- \frac{29 y}{7}$ into the numerator.

$\frac{- 7}{29} \cdot \frac{- 29 y}{7} = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.1.3

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{29} \cdot \frac{- 29 y}{7} = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.1.4

Cancel the common factor.

$\frac{7 \cdot - 1}{29} \cdot \frac{- 29 y}{7} = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{29} (- 29 y) = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.2

Cancel the common factor of $29$ .

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Step 3.4.1.1.2.1

Factor $29$ out of $- 29 y$ .

$\frac{- 1}{29} (29 (- y)) = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{29} (29 (- y)) = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.2.3

Rewrite the expression.

$- - y = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.3

Multiply.

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Step 3.4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{7}{29} \cdot \frac{29}{5}$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $- \frac{7}{29} \cdot \frac{29}{5}$ .

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Step 3.4.2.1.1

Cancel the common factor of $29$ .

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Step 3.4.2.1.1.1

Move the leading negative in $- \frac{7}{29}$ into the numerator.

$y = \frac{- 7}{29} \cdot \frac{29}{5}$

Step 3.4.2.1.1.2

Cancel the common factor.

$y = \frac{- 7}{29} \cdot \frac{29}{5}$

Step 3.4.2.1.1.3

Rewrite the expression.

$y = - 7 (\frac{1}{5})$

Step 3.4.2.1.2

Combine $- 7$ and $\frac{1}{5}$ .

$y = \frac{- 7}{5}$

Step 3.4.2.1.3

Move the negative in front of the fraction.

$y = - \frac{7}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{7}{5}$

Decimal Form:

$y = - 1.4$

Mixed Number Form:

$y = - 1 \frac{2}{5}$