Finite Math Examples

$\frac{m}{3} - 5 < \frac{7}{3} - \frac{m}{4}$

Step 1

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

Tap for more steps...

Step 1.1

Add $\frac{m}{4}$ to both sides of the inequality.

$\frac{m}{3} - 5 + \frac{m}{4} < \frac{7}{3}$

Step 1.2

To write $\frac{m}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{m}{3} \cdot \frac{4}{4} + \frac{m}{4} - 5 < \frac{7}{3}$

Step 1.3

To write $\frac{m}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{m}{3} \cdot \frac{4}{4} + \frac{m}{4} \cdot \frac{3}{3} - 5 < \frac{7}{3}$

Step 1.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.4.1

Multiply $\frac{m}{3}$ by $\frac{4}{4}$ .

$\frac{m \cdot 4}{3 \cdot 4} + \frac{m}{4} \cdot \frac{3}{3} - 5 < \frac{7}{3}$

Step 1.4.2

Multiply $3$ by $4$ .

$\frac{m \cdot 4}{12} + \frac{m}{4} \cdot \frac{3}{3} - 5 < \frac{7}{3}$

Step 1.4.3

Multiply $\frac{m}{4}$ by $\frac{3}{3}$ .

$\frac{m \cdot 4}{12} + \frac{m \cdot 3}{4 \cdot 3} - 5 < \frac{7}{3}$

Step 1.4.4

Multiply $4$ by $3$ .

$\frac{m \cdot 4}{12} + \frac{m \cdot 3}{12} - 5 < \frac{7}{3}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{m \cdot 4 + m \cdot 3}{12} - 5 < \frac{7}{3}$

Step 1.6

Reorder $m$ and $3$ .

$\frac{4 \cdot m + 3 \cdot m}{12} - 5 < \frac{7}{3}$

Step 1.7

Add $4 \cdot m$ and $3 \cdot m$ .

$\frac{7 m}{12} - 5 < \frac{7}{3}$

Step 2

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

Tap for more steps...

Step 2.1

Add $5$ to both sides of the inequality.

$\frac{7 m}{12} < \frac{7}{3} + 5$

Step 2.2

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

$\frac{7 m}{12} < \frac{7}{3} + 5 \cdot \frac{3}{3}$

Step 2.3

Combine $5$ and $\frac{3}{3}$ .

$\frac{7 m}{12} < \frac{7}{3} + \frac{5 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{7 m}{12} < \frac{7 + 5 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Multiply $5$ by $3$ .

$\frac{7 m}{12} < \frac{7 + 15}{3}$

Step 2.5.2

Add $7$ and $15$ .

$\frac{7 m}{12} < \frac{22}{3}$

Step 3

Multiply both sides by $12$ .

$\frac{7 m}{12} \cdot 12 < \frac{22}{3} \cdot 12$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the left side.

Tap for more steps...

Step 4.1.1

Cancel the common factor of $12$ .

Tap for more steps...

Step 4.1.1.1

Cancel the common factor.

$\frac{7 m}{12} \cdot 12 < \frac{22}{3} \cdot 12$

Step 4.1.1.2

Rewrite the expression.

$7 m < \frac{22}{3} \cdot 12$

Step 4.2

Simplify the right side.

Tap for more steps...

Step 4.2.1

Simplify $\frac{22}{3} \cdot 12$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1.1

Factor $3$ out of $12$ .

$7 m < \frac{22}{3} \cdot (3 (4))$

Step 4.2.1.1.2

Cancel the common factor.

$7 m < \frac{22}{3} \cdot (3 \cdot 4)$

Step 4.2.1.1.3

Rewrite the expression.

$7 m < 22 \cdot 4$

Step 4.2.1.2

Multiply $22$ by $4$ .

$7 m < 88$

Step 5

Divide each term in $7 m < 88$ by $7$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $7 m < 88$ by $7$ .

$\frac{7 m}{7} < \frac{88}{7}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $7$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{7 m}{7} < \frac{88}{7}$

Step 5.2.1.2

Divide $m$ by $1$ .

$m < \frac{88}{7}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$m < \frac{88}{7}$

Interval Notation:

$(- \infty, \frac{88}{7})$