Solve the Inequality for x 5x-6y<2y-x+8

$5 x - 6 y < 2 y - x + 8$

Step 1

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

Add $x$ to both sides of the inequality.

$5 x - 6 y + x < 2 y + 8$

Add $5 x$ and $x$ .

$6 x - 6 y < 2 y + 8$

Step 2

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

Add $6 y$ to both sides of the inequality.

$6 x < 2 y + 8 + 6 y$

Add $2 y$ and $6 y$ .

$6 x < 8 y + 8$

Step 3

Divide each term in $6 x < 8 y + 8$ by $6$ and simplify.

Divide each term in $6 x < 8 y + 8$ by $6$ .

$\frac{6 x}{6} < \frac{8 y}{6} + \frac{8}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} < \frac{8 y}{6} + \frac{8}{6}$

Divide $x$ by $1$ .

$x < \frac{8 y}{6} + \frac{8}{6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8 y$ .

$x < \frac{2 (4 y)}{6} + \frac{8}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x < \frac{2 (4 y)}{2 (3)} + \frac{8}{6}$

Cancel the common factor.

$x < \frac{2 (4 y)}{2 \cdot 3} + \frac{8}{6}$

Rewrite the expression.

$x < \frac{4 y}{3} + \frac{8}{6}$

Cancel the common factor of $8$ and $6$ .

Factor $2$ out of $8$ .

$x < \frac{4 y}{3} + \frac{2 (4)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x < \frac{4 y}{3} + \frac{2 \cdot 4}{2 \cdot 3}$

Cancel the common factor.

$x < \frac{4 y}{3} + \frac{2 \cdot 4}{2 \cdot 3}$

Rewrite the expression.

$x < \frac{4 y}{3} + \frac{4}{3}$