Pre-Algebra Examples

$2 n - 3 (n - 4) < 5 n - 36$

Step 1

Simplify $2 n - 3 (n - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 n - 3 n - 3 \cdot - 4 < 5 n - 36$

Step 1.1.2

Multiply $- 3$ by $- 4$ .

$2 n - 3 n + 12 < 5 n - 36$

Step 1.2

Subtract $3 n$ from $2 n$ .

$- n + 12 < 5 n - 36$

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.

$- n + 12 - 5 n < - 36$

Step 2.2

Subtract $5 n$ from $- n$ .

$- 6 n + 12 < - 36$

Step 3

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

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Step 3.1

Subtract $12$ from both sides of the inequality.

$- 6 n < - 36 - 12$

Step 3.2

Subtract $12$ from $- 36$ .

$- 6 n < - 48$

Step 4

Divide each term in $- 6 n < - 48$ by $- 6$ and simplify.

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Step 4.1

Divide each term in $- 6 n < - 48$ by $- 6$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 6 n}{- 6} > \frac{- 48}{- 6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 6 n}{- 6} > \frac{- 48}{- 6}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n > \frac{- 48}{- 6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 48$ by $- 6$ .

$n > 8$

Step 5