Pre-Algebra Examples

$2 (3 n + 7) > 5$

Step 1

Divide each term in $2 (3 n + 7) > 5$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 (3 n + 7) > 5$ by $2$ .

$\frac{2 (3 n + 7)}{2} > \frac{5}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 (3 n + 7)}{2} > \frac{5}{2}$

Step 1.2.1.2

Divide $3 n + 7$ by $1$ .

$3 n + 7 > \frac{5}{2}$

Step 2

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

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Step 2.1

Subtract $7$ from both sides of the inequality.

$3 n > \frac{5}{2} - 7$

Step 2.2

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 n > \frac{5}{2} - 7 \cdot \frac{2}{2}$

Step 2.3

Combine $- 7$ and $\frac{2}{2}$ .

$3 n > \frac{5}{2} + \frac{- 7 \cdot 2}{2}$

Step 2.4

Combine the numerators over the common denominator.

$3 n > \frac{5 - 7 \cdot 2}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 7$ by $2$ .

$3 n > \frac{5 - 14}{2}$

Step 2.5.2

Subtract $14$ from $5$ .

$3 n > \frac{- 9}{2}$

Step 2.6

Move the negative in front of the fraction.

$3 n > - \frac{9}{2}$

Step 3

Divide each term in $3 n > - \frac{9}{2}$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 n > - \frac{9}{2}$ by $3$ .

$\frac{3 n}{3} > \frac{- \frac{9}{2}}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 n}{3} > \frac{- \frac{9}{2}}{3}$

Step 3.2.1.2

Divide $n$ by $1$ .

$n > \frac{- \frac{9}{2}}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Multiply the numerator by the reciprocal of the denominator.

$n > - \frac{9}{2} \cdot \frac{1}{3}$

Step 3.3.2

Cancel the common factor of $3$ .

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Step 3.3.2.1

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$n > \frac{- 9}{2} \cdot \frac{1}{3}$

Step 3.3.2.2

Factor $3$ out of $- 9$ .

$n > \frac{3 (- 3)}{2} \cdot \frac{1}{3}$

Step 3.3.2.3

Cancel the common factor.

$n > \frac{3 \cdot - 3}{2} \cdot \frac{1}{3}$

Step 3.3.2.4

Rewrite the expression.

$n > \frac{- 3}{2}$

Step 3.3.3

Move the negative in front of the fraction.

$n > - \frac{3}{2}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n > - \frac{3}{2}$

Interval Notation:

$(- \frac{3}{2}, \infty)$