Solve the System of @WORD y<7x+2y>7x-3

$y < 7 x + 2 y > 7 x - 3$

Step 1

Solve $y < 7 x + 2 y$ for $y$ .

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

Subtract $2 y$ from both sides of the inequality.

$y - 2 y < 7 x$

Subtract $2 y$ from $y$ .

$- y < 7 x$

Divide each term in $- y < 7 x$ by $- 1$ and simplify.

Divide each term in $- y < 7 x$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{7 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{7 x}{- 1}$

Divide $y$ by $1$ .

$y > \frac{7 x}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{7 x}{- 1}$ .

$y > - 1 \cdot (7 x)$

Rewrite $- 1 \cdot (7 x)$ as $- (7 x)$ .

$y > - (7 x)$

Multiply $7$ by $- 1$ .

$y > - 7 x$

Step 2

Solve $7 x + 2 y > 7 x - 3$ for $y$ .

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

Subtract $7 x$ from both sides of the inequality.

$2 y > 7 x - 3 - 7 x$

Combine the opposite terms in $7 x - 3 - 7 x$ .

Subtract $7 x$ from $7 x$ .

$2 y > 0 - 3$

Subtract $3$ from $0$ .

$2 y > - 3$

Divide each term in $2 y > - 3$ by $2$ and simplify.

Divide each term in $2 y > - 3$ by $2$ .

$\frac{2 y}{2} > \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} > \frac{- 3}{2}$

Divide $y$ by $1$ .

$y > \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$y > - \frac{3}{2}$

Step 3

Find the intersection of $y > - 7 x$ and $y > - \frac{3}{2}$ .

$y > - 7 x$ and $y > - \frac{3}{2}$

Step 4

Solve the System of @WORD y<7x+2y>7x-3

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