Question

$x + 5y < -30$

Explanation:

Step1: Isolate y in the inequality

Start by rearranging to solve for y.
$x + 5y < -30$
Subtract $x$ from both sides:
$5y < -x - 30$
Divide by 5:
$y < -\frac{1}{5}x - 6$

Step2: Identify boundary line

The boundary is the line $y = -\frac{1}{5}x - 6$. Since the inequality is $<$, use a dashed line.
Find intercepts:

• x-intercept: Set $y=0$:

$0 = -\frac{1}{5}x - 6 \implies x = -30$ (point $(-30, 0)$)

• y-intercept: Set $x=0$:

$y = -6$ (point $(0, -6)$)

Step3: Determine shaded region

Test a point not on the line, e.g., $(0,0)$:
$0 < -\frac{1}{5}(0) - 6 \implies 0 < -6$, which is false. So shade the region below the dashed line (opposite of the test point).

Answer:

1. Draw a dashed line through points $(-30, 0)$ and $(0, -6)$ (representing $y = -\frac{1}{5}x - 6$).
2. Shade all area below this dashed line; this shaded region represents the solution set of $x + 5y < -30$.