Precalculus Examples

$\frac{3 x - 1}{4} - \frac{x - 5}{5} > - 2$

Step 1

Simplify $\frac{3 x - 1}{4} - \frac{x - 5}{5}$ .

Tap for more steps...

Step 1.1

To write $\frac{3 x - 1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{3 x - 1}{4} \cdot \frac{5}{5} - \frac{x - 5}{5} > - 2$

Step 1.2

To write $- \frac{x - 5}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x - 1}{4} \cdot \frac{5}{5} - \frac{x - 5}{5} \cdot \frac{4}{4} > - 2$

Step 1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.3.1

Multiply $\frac{3 x - 1}{4}$ by $\frac{5}{5}$ .

$\frac{(3 x - 1) \cdot 5}{4 \cdot 5} - \frac{x - 5}{5} \cdot \frac{4}{4} > - 2$

Step 1.3.2

Multiply $4$ by $5$ .

$\frac{(3 x - 1) \cdot 5}{20} - \frac{x - 5}{5} \cdot \frac{4}{4} > - 2$

Step 1.3.3

Multiply $\frac{x - 5}{5}$ by $\frac{4}{4}$ .

$\frac{(3 x - 1) \cdot 5}{20} - \frac{(x - 5) \cdot 4}{5 \cdot 4} > - 2$

Step 1.3.4

Multiply $5$ by $4$ .

$\frac{(3 x - 1) \cdot 5}{20} - \frac{(x - 5) \cdot 4}{20} > - 2$

Step 1.4

Combine the numerators over the common denominator.

$\frac{(3 x - 1) \cdot 5 - (x - 5) \cdot 4}{20} > - 2$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Apply the distributive property.

$\frac{3 x \cdot 5 - 1 \cdot 5 - (x - 5) \cdot 4}{20} > - 2$

Step 1.5.2

Multiply $5$ by $3$ .

$\frac{15 x - 1 \cdot 5 - (x - 5) \cdot 4}{20} > - 2$

Step 1.5.3

Multiply $- 1$ by $5$ .

$\frac{15 x - 5 - (x - 5) \cdot 4}{20} > - 2$

Step 1.5.4

Apply the distributive property.

$\frac{15 x - 5 + (- x - - 5) \cdot 4}{20} > - 2$

Step 1.5.5

Multiply $- 1$ by $- 5$ .

$\frac{15 x - 5 + (- x + 5) \cdot 4}{20} > - 2$

Step 1.5.6

Apply the distributive property.

$\frac{15 x - 5 - x \cdot 4 + 5 \cdot 4}{20} > - 2$

Step 1.5.7

Multiply $4$ by $- 1$ .

$\frac{15 x - 5 - 4 x + 5 \cdot 4}{20} > - 2$

Step 1.5.8

Multiply $5$ by $4$ .

$\frac{15 x - 5 - 4 x + 20}{20} > - 2$

Step 1.5.9

Subtract $4 x$ from $15 x$ .

$\frac{11 x - 5 + 20}{20} > - 2$

Step 1.5.10

Add $- 5$ and $20$ .

$\frac{11 x + 15}{20} > - 2$

Step 2

Multiply both sides by $20$ .

$\frac{11 x + 15}{20} \cdot 20 > - 2 \cdot 20$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Cancel the common factor of $20$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor.

$\frac{11 x + 15}{20} \cdot 20 > - 2 \cdot 20$

Step 3.1.1.2

Rewrite the expression.

$11 x + 15 > - 2 \cdot 20$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 2$ by $20$ .

$11 x + 15 > - 40$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Subtract $15$ from both sides of the inequality.

$11 x > - 40 - 15$

Step 4.1.2

Subtract $15$ from $- 40$ .

$11 x > - 55$

Step 4.2

Divide each term in $11 x > - 55$ by $11$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $11 x > - 55$ by $11$ .

$\frac{11 x}{11} > \frac{- 55}{11}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $11$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{11 x}{11} > \frac{- 55}{11}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x > \frac{- 55}{11}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Divide $- 55$ by $11$ .

$x > - 5$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > - 5$

Interval Notation:

$(- 5, \infty)$