Solve the System of Inequalities 1/4y<-1 or 3+y>=5

$\frac{1}{4} y < - 1$ or $3 + y \geq 5$

Multiply each term in $\frac{1}{4} y < - 1$ by $4$ to eliminate the fractions.

Multiply each term in $\frac{1}{4} y < - 1$ by $4$ .

$\frac{1}{4} y \cdot 4 < - 1 \cdot 4$ or $3 + y \geq 5$

Simplify the left side.

Combine $\frac{1}{4}$ and $y$ .

$\frac{y}{4} \cdot 4 < - 1 \cdot 4$ or $3 + y \geq 5$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{y}{4} \cdot 4 < - 1 \cdot 4$ or $3 + y \geq 5$

Rewrite the expression.

$y < - 1 \cdot 4$ or $3 + y \geq 5$

Simplify the right side.

Multiply $- 1$ by $4$ .

$y < - 4$ or $3 + y \geq 5$

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

Subtract $3$ from both sides of the inequality.

$y < - 4$ or $y \geq 5 - 3$

Subtract $3$ from $5$ .

$y < - 4$ or $y \geq 2$

The result can be shown in multiple forms.

Inequality Form:

$y < - 4 or y \geq 2$

Interval Notation:

$(- \infty, - 4) \cup [2, \infty)$