Trigonometry Examples

$14 x + 11 < - 14 y + 11$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

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

$- 14 y + 11 > 14 x + 11$

Step 1.2

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

Tap for more steps...

Step 1.2.1

Subtract $11$ from both sides of the inequality.

$- 14 y > 14 x + 11 - 11$

Step 1.2.2

Combine the opposite terms in $14 x + 11 - 11$ .

Tap for more steps...

Step 1.2.2.1

Subtract $11$ from $11$ .

$- 14 y > 14 x + 0$

Step 1.2.2.2

Add $14 x$ and $0$ .

$- 14 y > 14 x$

Step 1.3

Divide each term in $- 14 y > 14 x$ by $- 14$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $- 14 y > 14 x$ by $- 14$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 14 y}{- 14} < \frac{14 x}{- 14}$

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Cancel the common factor of $- 14$ .

Tap for more steps...

Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 14 y}{- 14} < \frac{14 x}{- 14}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y < \frac{14 x}{- 14}$

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Cancel the common factor of $14$ and $- 14$ .

Tap for more steps...

Step 1.3.3.1.1

Factor $14$ out of $14 x$ .

$y < \frac{14 (x)}{- 14}$

Step 1.3.3.1.2

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

$y < - 1 \cdot x$

Step 1.3.3.2

Rewrite $- 1 \cdot x$ as $- x$ .

$y < - x$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

Tap for more steps...

Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 1$

$b = 0$

Step 2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 1$

y-intercept: $(0, 0)$

Slope: $- 1$

y-intercept: $(0, 0)$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- x$ .

$y < - x$

Step 4