Solve the System of @WORD x<=-3y<5/3x+2

$x \leq - 3 y < \frac{5}{3} x + 2$

Step 1

Solve $x \leq - 3 y$ for $y$ .

Rewrite so $y$ is on the left side of the inequality.

$- 3 y \geq x$

Divide each term in $- 3 y \geq x$ by $- 3$ and simplify.

Divide each term in $- 3 y \geq x$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} \leq \frac{x}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} \leq \frac{x}{- 3}$

Divide $y$ by $1$ .

$y \leq \frac{x}{- 3}$

Simplify the right side.

Move the negative in front of the fraction.

$y \leq - \frac{x}{3}$

Step 2

Divide each term in $- 3 y < \frac{5}{3} x + 2$ by $- 3$ and simplify.

Divide each term in $- 3 y < \frac{5}{3} x + 2$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 y}{- 3} > \frac{\frac{5}{3} x}{- 3} + \frac{2}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} > \frac{\frac{5}{3} x}{- 3} + \frac{2}{- 3}$

Divide $y$ by $1$ .

$y > \frac{\frac{5}{3} x}{- 3} + \frac{2}{- 3}$

Simplify the right side.

Simplify each term.

Combine $\frac{5}{3}$ and $x$ .

$y > \frac{\frac{5 x}{3}}{- 3} + \frac{2}{- 3}$

Multiply the numerator by the reciprocal of the denominator.

$y > \frac{5 x}{3} \cdot \frac{1}{- 3} + \frac{2}{- 3}$

Move the negative in front of the fraction.

$y > \frac{5 x}{3} (- \frac{1}{3}) + \frac{2}{- 3}$

Multiply $\frac{5 x}{3} (- \frac{1}{3})$ .

Multiply $\frac{5 x}{3}$ by $\frac{1}{3}$ .

$y > - \frac{5 x}{3 \cdot 3} + \frac{2}{- 3}$

Multiply $3$ by $3$ .

$y > - \frac{5 x}{9} + \frac{2}{- 3}$

Move the negative in front of the fraction.

$y > - \frac{5 x}{9} - \frac{2}{3}$

Step 3

Find the intersection of $y \leq - \frac{x}{3}$ and $y > - \frac{5 x}{9} - \frac{2}{3}$ .

$- \frac{5 x}{9} - \frac{2}{3} < y \leq - \frac{x}{3}$

Step 4

Solve the System of @WORD x<=-3y<5/3x+2

Related Questions

Support LCMGCF.com by disabling your adblocker.