Solve the Inequality for k 4k+2(3k+8)<3k+10-8

$4 k + 2 (3 k + 8) < 3 k + 10 - 8$

Simplify $4 k + 2 (3 k + 8)$ .

Simplify each term.

Apply the distributive property.

$4 k + 2 (3 k) + 2 \cdot 8 < 3 k + 10 - 8$

Multiply $3$ by $2$ .

$4 k + 6 k + 2 \cdot 8 < 3 k + 10 - 8$

Multiply $2$ by $8$ .

$4 k + 6 k + 16 < 3 k + 10 - 8$

Add $4 k$ and $6 k$ .

$10 k + 16 < 3 k + 10 - 8$

Subtract $8$ from $10$ .

$10 k + 16 < 3 k + 2$

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

Subtract $3 k$ from both sides of the inequality.

$10 k + 16 - 3 k < 2$

Subtract $3 k$ from $10 k$ .

$7 k + 16 < 2$

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

Subtract $16$ from both sides of the inequality.

$7 k < 2 - 16$

Subtract $16$ from $2$ .

$7 k < - 14$

Divide each term in $7 k < - 14$ by $7$ and simplify.

Divide each term in $7 k < - 14$ by $7$ .

$\frac{7 k}{7} < \frac{- 14}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 k}{7} < \frac{- 14}{7}$

Divide $k$ by $1$ .

$k < \frac{- 14}{7}$

Simplify the right side.

Divide $- 14$ by $7$ .

$k < - 2$

The result can be shown in multiple forms.

Inequality Form:

$k < - 2$

Interval Notation:

$(- \infty, - 2)$