Algebra Examples

$- \frac{1}{2} \leq \frac{x}{4} - 4 < 6$

Step 1

Add $4$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- \frac{1}{2} + 4 \leq \frac{x}{4} < 6 + 4$

Step 2

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{2} + 4 \cdot \frac{2}{2} \leq \frac{x}{4} < 6 + 4$

Step 3

Combine $4$ and $\frac{2}{2}$ .

$- \frac{1}{2} + \frac{4 \cdot 2}{2} \leq \frac{x}{4} < 6 + 4$

Step 4

Combine the numerators over the common denominator.

$\frac{- 1 + 4 \cdot 2}{2} \leq \frac{x}{4} < 6 + 4$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $4$ by $2$ .

$\frac{- 1 + 8}{2} \leq \frac{x}{4} < 6 + 4$

Step 5.2

Add $- 1$ and $8$ .

$\frac{7}{2} \leq \frac{x}{4} < 6 + 4$

Step 6

Multiply each term in the inequality by $4$ .

$\frac{7}{2} \cdot 4 \leq \frac{x}{4} \cdot 4 < 6 \cdot 4 + 4 \cdot 4$

Step 7

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.1

Factor $2$ out of $4$ .

$\frac{7}{2} \cdot (2 (2)) \leq \frac{x}{4} \cdot 4 < 6 \cdot 4 + 4 \cdot 4$

Step 7.2

Cancel the common factor.

$\frac{7}{2} \cdot (2 \cdot 2) \leq \frac{x}{4} \cdot 4 < 6 \cdot 4 + 4 \cdot 4$

Step 7.3

Rewrite the expression.

$7 \cdot 2 \leq \frac{x}{4} \cdot 4 < 6 \cdot 4 + 4 \cdot 4$

Step 8

Multiply $7$ by $2$ .

$14 \leq \frac{x}{4} \cdot 4 < 6 \cdot 4 + 4 \cdot 4$

Step 9

Cancel the common factor of $4$ .

Tap for more steps...

Step 9.1

Cancel the common factor.

$14 \leq \frac{x}{4} \cdot 4 < 6 \cdot 4 + 4 \cdot 4$

Step 9.2

Rewrite the expression.

$14 \leq x < 6 \cdot 4 + 4 \cdot 4$

Step 10

Simplify each term.

Tap for more steps...

Step 10.1

Multiply $6$ by $4$ .

$14 \leq x < 24 + 4 \cdot 4$

Step 10.2

Multiply $4$ by $4$ .

$14 \leq x < 24 + 16$

Step 11

Add $24$ and $16$ .

$14 \leq x < 40$

Step 12

The result can be shown in multiple forms.

Inequality Form:

$14 \leq x < 40$

Interval Notation:

$[14, 40)$

Step 13