Finite Math Examples

$\frac{2 x - 5}{8} > \frac{x + 4}{3}$

Step 1

Multiply both sides by $8$ .

$\frac{2 x - 5}{8} \cdot 8 > \frac{x + 4}{3} \cdot 8$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor.

$\frac{2 x - 5}{8} \cdot 8 > \frac{x + 4}{3} \cdot 8$

Step 2.1.1.2

Rewrite the expression.

$2 x - 5 > \frac{x + 4}{3} \cdot 8$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $\frac{x + 4}{3} \cdot 8$ .

Tap for more steps...

Step 2.2.1.1

Combine $\frac{x + 4}{3}$ and $8$ .

$2 x - 5 > \frac{(x + 4) \cdot 8}{3}$

Step 2.2.1.2

Move $8$ to the left of $x + 4$ .

$2 x - 5 > \frac{8 (x + 4)}{3}$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Multiply both sides by $3$ .

$(2 x - 5) \cdot 3 > \frac{8 (x + 4)}{3} \cdot 3$

Step 3.2

Simplify.

Tap for more steps...

Step 3.2.1

Simplify the left side.

Tap for more steps...

Step 3.2.1.1

Simplify $(2 x - 5) \cdot 3$ .

Tap for more steps...

Step 3.2.1.1.1

Apply the distributive property.

$2 x \cdot 3 - 5 \cdot 3 > \frac{8 (x + 4)}{3} \cdot 3$

Step 3.2.1.1.2

Multiply.

Tap for more steps...

Step 3.2.1.1.2.1

Multiply $3$ by $2$ .

$6 x - 5 \cdot 3 > \frac{8 (x + 4)}{3} \cdot 3$

Step 3.2.1.1.2.2

Multiply $- 5$ by $3$ .

$6 x - 15 > \frac{8 (x + 4)}{3} \cdot 3$

Step 3.2.2

Simplify the right side.

Tap for more steps...

Step 3.2.2.1

Simplify $\frac{8 (x + 4)}{3} \cdot 3$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.2.1.1.1

Cancel the common factor.

$6 x - 15 > \frac{8 (x + 4)}{3} \cdot 3$

Step 3.2.2.1.1.2

Rewrite the expression.

$6 x - 15 > 8 (x + 4)$

Step 3.2.2.1.2

Apply the distributive property.

$6 x - 15 > 8 x + 8 \cdot 4$

Step 3.2.2.1.3

Multiply $8$ by $4$ .

$6 x - 15 > 8 x + 32$

Step 3.3

Solve for $x$ .

Tap for more steps...

Step 3.3.1

Move all terms containing $x$ to the left side of the inequality.

Tap for more steps...

Step 3.3.1.1

Subtract $8 x$ from both sides of the inequality.

$6 x - 15 - 8 x > 32$

Step 3.3.1.2

Subtract $8 x$ from $6 x$ .

$- 2 x - 15 > 32$

Step 3.3.2

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

Tap for more steps...

Step 3.3.2.1

Add $15$ to both sides of the inequality.

$- 2 x > 32 + 15$

Step 3.3.2.2

Add $32$ and $15$ .

$- 2 x > 47$

Step 3.3.3

Divide each term in $- 2 x > 47$ by $- 2$ and simplify.

Tap for more steps...

Step 3.3.3.1

Divide each term in $- 2 x > 47$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} < \frac{47}{- 2}$

Step 3.3.3.2

Simplify the left side.

Tap for more steps...

Step 3.3.3.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 3.3.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} < \frac{47}{- 2}$

Step 3.3.3.2.1.2

Divide $x$ by $1$ .

$x < \frac{47}{- 2}$

Step 3.3.3.3

Simplify the right side.

Tap for more steps...

Step 3.3.3.3.1

Move the negative in front of the fraction.

$x < - \frac{47}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{47}{2}$

Interval Notation:

$(- \infty, - \frac{47}{2})$