Solve for k 17+12k>=k-2>=12k+14

$17 + 12 k \geq k - 2 \geq 12 k + 14$

Step 1

Solve $17 + 12 k \geq k - 2$ for $k$ .

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

Subtract $k$ from both sides of the inequality.

$17 + 12 k - k \geq - 2$

Subtract $k$ from $12 k$ .

$17 + 11 k \geq - 2$

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

Subtract $17$ from both sides of the inequality.

$11 k \geq - 2 - 17$

Subtract $17$ from $- 2$ .

$11 k \geq - 19$

Divide each term in $11 k \geq - 19$ by $11$ and simplify.

Divide each term in $11 k \geq - 19$ by $11$ .

$\frac{11 k}{11} \geq \frac{- 19}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 k}{11} \geq \frac{- 19}{11}$

Divide $k$ by $1$ .

$k \geq \frac{- 19}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$k \geq - \frac{19}{11}$

Step 2

Solve $k - 2 \geq 12 k + 14$ for $k$ .

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

Subtract $12 k$ from both sides of the inequality.

$k - 2 - 12 k \geq 14$

Subtract $12 k$ from $k$ .

$- 11 k - 2 \geq 14$

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

Add $2$ to both sides of the inequality.

$- 11 k \geq 14 + 2$

Add $14$ and $2$ .

$- 11 k \geq 16$

Divide each term in $- 11 k \geq 16$ by $- 11$ and simplify.

Divide each term in $- 11 k \geq 16$ by $- 11$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 11 k}{- 11} \leq \frac{16}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 k}{- 11} \leq \frac{16}{- 11}$

Divide $k$ by $1$ .

$k \leq \frac{16}{- 11}$

Simplify the right side.

Move the negative in front of the fraction.

$k \leq - \frac{16}{11}$

Step 3

Find the intersection of $k \geq - \frac{19}{11}$ and $k \leq - \frac{16}{11}$ .

$- \frac{19}{11} \leq k \leq - \frac{16}{11}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- \frac{19}{11} \leq k \leq - \frac{16}{11}$

Interval Notation:

$[- \frac{19}{11}, - \frac{16}{11}]$

Step 5

Solve for k 17+12k>=k-2>=12k+14

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