Algebra Examples

$- \frac{1}{4} x - 8 < \frac{3}{4}$

Step 1

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

$- \frac{x}{4} - 8 < \frac{3}{4}$

Step 2

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

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Step 2.1

Add $8$ to both sides of the inequality.

$- \frac{x}{4} < \frac{3}{4} + 8$

Step 2.2

To write $8$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{x}{4} < \frac{3}{4} + 8 \cdot \frac{4}{4}$

Step 2.3

Combine $8$ and $\frac{4}{4}$ .

$- \frac{x}{4} < \frac{3}{4} + \frac{8 \cdot 4}{4}$

Step 2.4

Combine the numerators over the common denominator.

$- \frac{x}{4} < \frac{3 + 8 \cdot 4}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $8$ by $4$ .

$- \frac{x}{4} < \frac{3 + 32}{4}$

Step 2.5.2

Add $3$ and $32$ .

$- \frac{x}{4} < \frac{35}{4}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- x < 35$

Step 4

Divide each term in $- x < 35$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- x < 35$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{35}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{35}{- 1}$

Step 4.2.2

Divide $x$ by $1$ .

$x > \frac{35}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $35$ by $- 1$ .

$x > - 35$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - 35$

Interval Notation:

$(- 35, \infty)$