Algebra Examples

$2 (3 n + 7) > 5 n$

Step 1

Simplify $2 (3 n + 7)$ .

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Step 1.1

Rewrite.

$0 + 0 + 2 (3 n + 7) > 5 n$

Step 1.2

Simplify by adding zeros.

$2 (3 n + 7) > 5 n$

Step 1.3

Apply the distributive property.

$2 (3 n) + 2 \cdot 7 > 5 n$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $3$ by $2$ .

$6 n + 2 \cdot 7 > 5 n$

Step 1.4.2

Multiply $2$ by $7$ .

$6 n + 14 > 5 n$

Step 2

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

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Step 2.1

Subtract $5 n$ from both sides of the inequality.

$6 n + 14 - 5 n > 0$

Step 2.2

Subtract $5 n$ from $6 n$ .

$n + 14 > 0$

Step 3

Subtract $14$ from both sides of the inequality.

$n > - 14$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n > - 14$

Interval Notation:

$(- 14, \infty)$