Algebra Examples

$\frac{1}{4} (8 - x) > - 3$

Step 1

Simplify $\frac{1}{4} \cdot (8 - x)$ .

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Step 1.1

Apply the distributive property.

$\frac{1}{4} \cdot 8 + \frac{1}{4} (- x) > - 3$

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Factor $4$ out of $8$ .

$\frac{1}{4} \cdot (4 (2)) + \frac{1}{4} (- x) > - 3$

Step 1.2.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 \cdot 2) + \frac{1}{4} (- x) > - 3$

Step 1.2.3

Rewrite the expression.

$2 + \frac{1}{4} (- x) > - 3$

Step 1.3

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

$2 - \frac{x}{4} > - 3$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the inequality.

$- \frac{x}{4} > - 3 - 2$

Step 2.2

Subtract $2$ from $- 3$ .

$- \frac{x}{4} > - 5$

Step 3

Divide each term in $- \frac{x}{4} > - 5$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{x}{4} > - 5$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- \frac{x}{4}}{- 1} < \frac{- 5}{- 1}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{\frac{x}{4}}{1} < \frac{- 5}{- 1}$

Step 3.2.2

Divide $\frac{x}{4}$ by $1$ .

$\frac{x}{4} < \frac{- 5}{- 1}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 5$ by $- 1$ .

$\frac{x}{4} < 5$

Step 4

Multiply both sides by $4$ .

$\frac{x}{4} \cdot 4 < 5 \cdot 4$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $4$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{x}{4} \cdot 4 < 5 \cdot 4$

Step 5.1.1.2

Rewrite the expression.

$x < 5 \cdot 4$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $5$ by $4$ .

$x < 20$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x < 20$

Interval Notation:

$(- \infty, 20)$