Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Simplify the left side.

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factor of $4$ .

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Step 1.2.2.1

Cancel the common factor.

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

Step 1.2.2.2

Rewrite the expression.

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply $- 1$ by $4$ .

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

Step 2

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

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Step 2.1

Subtract $3$ from both sides of the inequality.

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

Step 2.2

Subtract $3$ from $5$ .

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

Step 3

The result can be shown in multiple forms.

Inequality Form:

$y < - 4 or y \geq 2$

Interval Notation:

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

Step 4