Pre-Algebra Examples

$y + 8 - 2 (y - 20) > 0$

Step 1

Simplify $y + 8 - 2 (y - 20)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$y + 8 - 2 y - 2 \cdot - 20 > 0$

Step 1.1.2

Multiply $- 2$ by $- 20$ .

$y + 8 - 2 y + 40 > 0$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $2 y$ from $y$ .

$- y + 8 + 40 > 0$

Step 1.2.2

Add $8$ and $40$ .

$- y + 48 > 0$

Step 2

Subtract $48$ from both sides of the inequality.

$- y > - 48$

Step 3

Divide each term in $- y > - 48$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y > - 48$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} < \frac{- 48}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} < \frac{- 48}{- 1}$

Step 3.2.2

Divide $y$ by $1$ .

$y < \frac{- 48}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 48$ by $- 1$ .

$y < 48$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$y < 48$

Interval Notation:

$(- \infty, 48)$