Basic Math Examples

$\frac{5 y - 5}{2} + \frac{7}{4} = \frac{10 y + 7}{4}$

Step 1

Multiply both sides by $4$ .

$(\frac{5 y - 5}{2} + \frac{7}{4}) \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Simplify $(\frac{5 y - 5}{2} + \frac{7}{4}) \cdot 4$ .

Tap for more steps...

Step 2.1.1.1

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

Tap for more steps...

Step 2.1.1.1.1

Factor $5$ out of $5 y$ .

$(\frac{5 (y) - 5}{2} + \frac{7}{4}) \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.1.2

Factor $5$ out of $- 5$ .

$(\frac{5 (y) + 5 (- 1)}{2} + \frac{7}{4}) \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.1.3

Factor $5$ out of $5 (y) + 5 (- 1)$ .

$(\frac{5 (y - 1)}{2} + \frac{7}{4}) \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.2

To write $\frac{5 (y - 1)}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{5 (y - 1)}{2} \cdot \frac{2}{2} + \frac{7}{4}) \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.1.1.3.1

Multiply $\frac{5 (y - 1)}{2}$ by $\frac{2}{2}$ .

$(\frac{5 (y - 1) \cdot 2}{2 \cdot 2} + \frac{7}{4}) \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.3.2

Multiply $2$ by $2$ .

$(\frac{5 (y - 1) \cdot 2}{4} + \frac{7}{4}) \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{5 (y - 1) \cdot 2 + 7}{4} \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.5

Simplify the numerator.

Tap for more steps...

Step 2.1.1.5.1

Apply the distributive property.

$\frac{(5 y + 5 \cdot - 1) \cdot 2 + 7}{4} \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.5.2

Multiply $5$ by $- 1$ .

$\frac{(5 y - 5) \cdot 2 + 7}{4} \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.5.3

Apply the distributive property.

$\frac{5 y \cdot 2 - 5 \cdot 2 + 7}{4} \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.5.4

Multiply $2$ by $5$ .

$\frac{10 y - 5 \cdot 2 + 7}{4} \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.5.5

Multiply $- 5$ by $2$ .

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

Step 2.1.1.5.6

Add $- 10$ and $7$ .

$\frac{10 y - 3}{4} \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.6

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.1.1.6.1

Cancel the common factor.

$\frac{10 y - 3}{4} \cdot 4 = \frac{10 y + 7}{4} \cdot 4$

Step 2.1.1.6.2

Rewrite the expression.

$10 y - 3 = \frac{10 y + 7}{4} \cdot 4$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$10 y - 3 = \frac{10 y + 7}{4} \cdot 4$

Step 2.2.1.2

Rewrite the expression.

$10 y - 3 = 10 y + 7$

Step 3

Solve for $y$ .

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

Subtract $10 y$ from both sides of the equation.

$10 y - 3 - 10 y = 7$

Step 3.1.2

Combine the opposite terms in $10 y - 3 - 10 y$ .

Tap for more steps...

Step 3.1.2.1

Subtract $10 y$ from $10 y$ .

$0 - 3 = 7$

Step 3.1.2.2

Subtract $3$ from $0$ .

$- 3 = 7$

Step 3.2

Since $- 3 \neq 7$ , there are no solutions.

No solution