Basic Math Examples

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

Step 1

Combine $\frac{4}{7}$ and $y$ .

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

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.

$\frac{4 y}{7} = 3 + 7$

Step 2.2

Add $3$ and $7$ .

$\frac{4 y}{7} = 10$

Step 3

Multiply both sides of the equation by $\frac{7}{4}$ .

$\frac{7}{4} \cdot \frac{4 y}{7} = \frac{7}{4} \cdot 10$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{7}{4} \cdot \frac{4 y}{7}$ .

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Step 4.1.1.1

Cancel the common factor of $7$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{7}{4} \cdot \frac{4 y}{7} = \frac{7}{4} \cdot 10$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{4} (4 y) = \frac{7}{4} \cdot 10$

Step 4.1.1.2

Cancel the common factor of $4$ .

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Step 4.1.1.2.1

Factor $4$ out of $4 y$ .

$\frac{1}{4} (4 (y)) = \frac{7}{4} \cdot 10$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{4} (4 y) = \frac{7}{4} \cdot 10$

Step 4.1.1.2.3

Rewrite the expression.

$y = \frac{7}{4} \cdot 10$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{7}{4} \cdot 10$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $4$ .

$y = \frac{7}{2 (2)} \cdot 10$

Step 4.2.1.1.2

Factor $2$ out of $10$ .

$y = \frac{7}{2 \cdot 2} \cdot (2 \cdot 5)$

Step 4.2.1.1.3

Cancel the common factor.

$y = \frac{7}{2 \cdot 2} \cdot (2 \cdot 5)$

Step 4.2.1.1.4

Rewrite the expression.

$y = \frac{7}{2} \cdot 5$

Step 4.2.1.2

Combine $\frac{7}{2}$ and $5$ .

$y = \frac{7 \cdot 5}{2}$

Step 4.2.1.3

Multiply $7$ by $5$ .

$y = \frac{35}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$y = \frac{35}{2}$

Decimal Form:

$y = 17.5$

Mixed Number Form:

$y = 17 \frac{1}{2}$