Solve the Inequality for y (2y)/5+y/10<-2

$\frac{2 y}{5} + \frac{y}{10} < - 2$

Step 1

Simplify $\frac{2 y}{5} + \frac{y}{10}$ .

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

$\frac{2 y}{5} \cdot \frac{2}{2} + \frac{y}{10} < - 2$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2 y}{5}$ by $\frac{2}{2}$ .

$\frac{2 y \cdot 2}{5 \cdot 2} + \frac{y}{10} < - 2$

Multiply $5$ by $2$ .

$\frac{2 y \cdot 2}{10} + \frac{y}{10} < - 2$

Combine the numerators over the common denominator.

$\frac{2 y \cdot 2 + y}{10} < - 2$

Simplify the numerator.

Factor $y$ out of $2 y \cdot 2 + y$ .

Factor $y$ out of $2 y \cdot 2$ .

$\frac{y (2 \cdot 2) + y}{10} < - 2$

Raise $y$ to the power of $1$ .

$\frac{y (2 \cdot 2) + y^{1}}{10} < - 2$

Factor $y$ out of $y^{1}$ .

$\frac{y (2 \cdot 2) + y \cdot 1}{10} < - 2$

Factor $y$ out of $y (2 \cdot 2) + y \cdot 1$ .

$\frac{y (2 \cdot 2 + 1)}{10} < - 2$

Multiply $2$ by $2$ .

$\frac{y (4 + 1)}{10} < - 2$

Add $4$ and $1$ .

$\frac{y \cdot 5}{10} < - 2$

Cancel the common factor of $5$ and $10$ .

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

$\frac{5 \cdot y}{10} < - 2$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 \cdot y}{5 \cdot 2} < - 2$

Cancel the common factor.

$\frac{5 \cdot y}{5 \cdot 2} < - 2$

Rewrite the expression.

$\frac{y}{2} < - 2$

Step 2

Multiply both sides by $2$ .

$\frac{y}{2} \cdot 2 < - 2 \cdot 2$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{y}{2} \cdot 2 < - 2 \cdot 2$

Rewrite the expression.

$y < - 2 \cdot 2$

Simplify the right side.

Multiply $- 2$ by $2$ .

$y < - 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < - 4$

Interval Notation:

$(- \infty, - 4)$

Solve the Inequality for y (2y)/5+y/10<-2

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