Solve the Inequality for n 6-4(6n+7)>=122

$6 - 4 (6 n + 7) \geq 122$

Step 1

Simplify $6 - 4 (6 n + 7)$ .

Simplify each term.

Apply the distributive property.

$6 - 4 (6 n) - 4 \cdot 7 \geq 122$

Multiply $6$ by $- 4$ .

$6 - 24 n - 4 \cdot 7 \geq 122$

Multiply $- 4$ by $7$ .

$6 - 24 n - 28 \geq 122$

Subtract $28$ from $6$ .

$- 24 n - 22 \geq 122$

Step 2

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

Add $22$ to both sides of the inequality.

$- 24 n \geq 122 + 22$

Add $122$ and $22$ .

$- 24 n \geq 144$

Step 3

Divide each term in $- 24 n \geq 144$ by $- 24$ and simplify.

Divide each term in $- 24 n \geq 144$ by $- 24$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 24 n}{- 24} \leq \frac{144}{- 24}$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 n}{- 24} \leq \frac{144}{- 24}$

Divide $n$ by $1$ .

$n \leq \frac{144}{- 24}$

Simplify the right side.

Divide $144$ by $- 24$ .

$n \leq - 6$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$n \leq - 6$

Interval Notation:

$(- \infty, - 6]$

Solve the Inequality for n 6-4(6n+7)>=122

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