Algebra Examples

$- 9 + 3 (7 N + 1) \leq 2 N - 1 + 5 N$

Step 1

Rewrite so $N$ is on the left side of the inequality.

$2 N - 1 + 5 N \geq - 9 + 3 (7 N + 1)$

Step 2

Add $2 N$ and $5 N$ .

$7 N - 1 \geq - 9 + 3 (7 N + 1)$

Step 3

Simplify $- 9 + 3 (7 N + 1)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$7 N - 1 \geq - 9 + 3 (7 N) + 3 \cdot 1$

Step 3.1.2

Multiply $7$ by $3$ .

$7 N - 1 \geq - 9 + 21 N + 3 \cdot 1$

Step 3.1.3

Multiply $3$ by $1$ .

$7 N - 1 \geq - 9 + 21 N + 3$

Step 3.2

Add $- 9$ and $3$ .

$7 N - 1 \geq 21 N - 6$

Step 4

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

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Step 4.1

Subtract $21 N$ from both sides of the inequality.

$7 N - 1 - 21 N \geq - 6$

Step 4.2

Subtract $21 N$ from $7 N$ .

$- 14 N - 1 \geq - 6$

Step 5

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

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Step 5.1

Add $1$ to both sides of the inequality.

$- 14 N \geq - 6 + 1$

Step 5.2

Add $- 6$ and $1$ .

$- 14 N \geq - 5$

Step 6

Divide each term in $- 14 N \geq - 5$ by $- 14$ and simplify.

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Step 6.1

Divide each term in $- 14 N \geq - 5$ by $- 14$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 14 N}{- 14} \leq \frac{- 5}{- 14}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- 14$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{- 14 N}{- 14} \leq \frac{- 5}{- 14}$

Step 6.2.1.2

Divide $N$ by $1$ .

$N \leq \frac{- 5}{- 14}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Dividing two negative values results in a positive value.

$N \leq \frac{5}{14}$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$N \leq \frac{5}{14}$

Interval Notation:

$(- \infty, \frac{5}{14}]$