Finite Math Examples

$- x + \frac{6}{7} < \frac{3}{28}$

Step 1

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

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Step 1.1

Subtract $\frac{6}{7}$ from both sides of the inequality.

$- x < \frac{3}{28} - \frac{6}{7}$

Step 1.2

To write $- \frac{6}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- x < \frac{3}{28} - \frac{6}{7} \cdot \frac{4}{4}$

Step 1.3

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{6}{7}$ by $\frac{4}{4}$ .

$- x < \frac{3}{28} - \frac{6 \cdot 4}{7 \cdot 4}$

Step 1.3.2

Multiply $7$ by $4$ .

$- x < \frac{3}{28} - \frac{6 \cdot 4}{28}$

Step 1.4

Combine the numerators over the common denominator.

$- x < \frac{3 - 6 \cdot 4}{28}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 6$ by $4$ .

$- x < \frac{3 - 24}{28}$

Step 1.5.2

Subtract $24$ from $3$ .

$- x < \frac{- 21}{28}$

Step 1.6

Cancel the common factor of $- 21$ and $28$ .

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Step 1.6.1

Factor $7$ out of $- 21$ .

$- x < \frac{7 (- 3)}{28}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $7$ out of $28$ .

$- x < \frac{7 \cdot - 3}{7 \cdot 4}$

Step 1.6.2.2

Cancel the common factor.

$- x < \frac{7 \cdot - 3}{7 \cdot 4}$

Step 1.6.2.3

Rewrite the expression.

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

Step 1.7

Move the negative in front of the fraction.

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

Step 2

Divide each term in $- x < - \frac{3}{4}$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- x < - \frac{3}{4}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

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

Step 2.2.2

Divide $x$ by $1$ .

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

Step 2.3

Simplify the right side.

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Step 2.3.1

Dividing two negative values results in a positive value.

$x > \frac{\frac{3}{4}}{1}$

Step 2.3.2

Divide $\frac{3}{4}$ by $1$ .

$x > \frac{3}{4}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{3}{4}$

Interval Notation:

$(\frac{3}{4}, \infty)$