Algebra Examples

3 (1) - 2 y \leq 4

$3 (1) - 2 y \leq 4$

Step 1

Multiply

3

$3$ by

1

$1$ .

3 - 2 y \leq 4

$3 - 2 y \leq 4$

Step 2

Move all terms not containing

y

$y$ to the right side of the inequality.

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Step 2.1

Subtract

3

$3$ from both sides of the inequality.

- 2 y \leq 4 - 3

$- 2 y \leq 4 - 3$

Step 2.2

Subtract

3

$3$ from

4

$4$ .

- 2 y \leq 1

$- 2 y \leq 1$

- 2 y \leq 1

$- 2 y \leq 1$

Step 3

Divide each term in

- 2 y \leq 1

$- 2 y \leq 1$ by

- 2

$- 2$ and simplify.

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Step 3.1

Divide each term in

- 2 y \leq 1

$- 2 y \leq 1$ by

- 2

$- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

\frac{- 2 y}{- 2} \geq \frac{1}{- 2}

$\frac{- 2 y}{- 2} \geq \frac{1}{- 2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} \geq \frac{1}{- 2}$

Step 3.2.1.2

Divide

$y$ by

$1$ .

$y \geq \frac{1}{- 2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move the negative in front of the fraction.

$y \geq - \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y \geq - \frac{1}{2}$

Interval Notation:

$[- \frac{1}{2}, \infty)$