Basic Math Examples

$\frac{15 y - 20}{2 y} = 7$

Step 1

Factor $5$ out of $15 y - 20$ .

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Step 1.1

Factor $5$ out of $15 y$ .

$\frac{5 (3 y) - 20}{2 y} = 7$

Step 1.2

Factor $5$ out of $- 20$ .

$\frac{5 (3 y) + 5 (- 4)}{2 y} = 7$

Step 1.3

Factor $5$ out of $5 (3 y) + 5 (- 4)$ .

$\frac{5 (3 y - 4)}{2 y} = 7$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$2 y, 1$

Step 2.2

The LCM of one and any expression is the expression.

$2 y$

Step 3

Multiply each term in $\frac{5 (3 y - 4)}{2 y} = 7$ by $2 y$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{5 (3 y - 4)}{2 y} = 7$ by $2 y$ .

$\frac{5 (3 y - 4)}{2 y} (2 y) = 7 (2 y)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Rewrite using the commutative property of multiplication.

$2 \frac{5 (3 y - 4)}{2 y} y = 7 (2 y)$

Step 3.2.2

Cancel the common factor of $2$ .

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Step 3.2.2.1

Factor $2$ out of $2 y$ .

$2 \frac{5 (3 y - 4)}{2 (y)} y = 7 (2 y)$

Step 3.2.2.2

Cancel the common factor.

$2 \frac{5 (3 y - 4)}{2 y} y = 7 (2 y)$

Step 3.2.2.3

Rewrite the expression.

$\frac{5 (3 y - 4)}{y} y = 7 (2 y)$

Step 3.2.3

Cancel the common factor of $y$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{5 (3 y - 4)}{y} y = 7 (2 y)$

Step 3.2.3.2

Rewrite the expression.

$5 (3 y - 4) = 7 (2 y)$

Step 3.2.4

Apply the distributive property.

$5 (3 y) + 5 \cdot - 4 = 7 (2 y)$

Step 3.2.5

Multiply.

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Step 3.2.5.1

Multiply $3$ by $5$ .

$15 y + 5 \cdot - 4 = 7 (2 y)$

Step 3.2.5.2

Multiply $5$ by $- 4$ .

$15 y - 20 = 7 (2 y)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply $2$ by $7$ .

$15 y - 20 = 14 y$

Step 4

Solve the equation.

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Step 4.1

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

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Step 4.1.1

Subtract $14 y$ from both sides of the equation.

$15 y - 20 - 14 y = 0$

Step 4.1.2

Subtract $14 y$ from $15 y$ .

$y - 20 = 0$

Step 4.2

Add $20$ to both sides of the equation.

$y = 20$