Algebra Examples

$- 2 (5 + 6 n) < 6 (8 - 2 n)$

Step 1

Simplify $- 2 (5 + 6 n)$ .

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Step 1.1

Rewrite.

$0 + 0 - 2 (5 + 6 n) < 6 (8 - 2 n)$

Step 1.2

Simplify by adding zeros.

$- 2 (5 + 6 n) < 6 (8 - 2 n)$

Step 1.3

Apply the distributive property.

$- 2 \cdot 5 - 2 (6 n) < 6 (8 - 2 n)$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $- 2$ by $5$ .

$- 10 - 2 (6 n) < 6 (8 - 2 n)$

Step 1.4.2

Multiply $6$ by $- 2$ .

$- 10 - 12 n < 6 (8 - 2 n)$

Step 2

Simplify $6 (8 - 2 n)$ .

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Step 2.1

Apply the distributive property.

$- 10 - 12 n < 6 \cdot 8 + 6 (- 2 n)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $6$ by $8$ .

$- 10 - 12 n < 48 + 6 (- 2 n)$

Step 2.2.2

Multiply $- 2$ by $6$ .

$- 10 - 12 n < 48 - 12 n$

Step 3

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

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Step 3.1

Add $12 n$ to both sides of the inequality.

$- 10 - 12 n + 12 n < 48$

Step 3.2

Combine the opposite terms in $- 10 - 12 n + 12 n$ .

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Step 3.2.1

Add $- 12 n$ and $12 n$ .

$- 10 + 0 < 48$

Step 3.2.2

Add $- 10$ and $0$ .

$- 10 < 48$

Step 4

Since $- 10 < 48$ , the inequality will always be true.

Always true

Step 5