Algebra Examples

$2 (n + 3) - 4 \leq 5 n - 1$

Step 1

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

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$2 n + 2 \cdot 3 - 4 \leq 5 n - 1$

Step 1.1.2

Multiply $2$ by $3$ .

$2 n + 6 - 4 \leq 5 n - 1$

Step 1.2

Subtract $4$ from $6$ .

$2 n + 2 \leq 5 n - 1$

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.

$2 n + 2 - 5 n \leq - 1$

Step 2.2

Subtract $5 n$ from $2 n$ .

$- 3 n + 2 \leq - 1$

Step 3

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

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Step 3.1

Subtract $2$ from both sides of the inequality.

$- 3 n \leq - 1 - 2$

Step 3.2

Subtract $2$ from $- 1$ .

$- 3 n \leq - 3$

Step 4

Divide each term in $- 3 n \leq - 3$ by $- 3$ and simplify.

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Step 4.1

Divide each term in $- 3 n \leq - 3$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 n}{- 3} \geq \frac{- 3}{- 3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 3 n}{- 3} \geq \frac{- 3}{- 3}$

Step 4.2.1.2

Divide $n$ by $1$ .

$n \geq \frac{- 3}{- 3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 3$ by $- 3$ .

$n \geq 1$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$n \geq 1$

Interval Notation:

$[1, \infty)$