Solve the Inequality for k 6k+4<-4k+6

$6 k + 4 < - 4 k + 6$

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

Add $4 k$ to both sides of the inequality.

$6 k + 4 + 4 k < 6$

Add $6 k$ and $4 k$ .

$10 k + 4 < 6$

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

Subtract $4$ from both sides of the inequality.

$10 k < 6 - 4$

Subtract $4$ from $6$ .

$10 k < 2$

Divide each term in $10 k < 2$ by $10$ and simplify.

Divide each term in $10 k < 2$ by $10$ .

$\frac{10 k}{10} < \frac{2}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 k}{10} < \frac{2}{10}$

Divide $k$ by $1$ .

$k < \frac{2}{10}$

Simplify the right side.

Cancel the common factor of $2$ and $10$ .

Factor $2$ out of $2$ .

$k < \frac{2 (1)}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$k < \frac{2 \cdot 1}{2 \cdot 5}$

Cancel the common factor.

$k < \frac{2 \cdot 1}{2 \cdot 5}$

Rewrite the expression.

$k < \frac{1}{5}$

The result can be shown in multiple forms.

Inequality Form:

$k < \frac{1}{5}$

Interval Notation:

$(- \infty, \frac{1}{5})$