Question

solve the inequality and graph the solution.
26 + 14y ≤ -30
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Isolate the term with y

Subtract 26 from both sides of the inequality $26 + 14y\leq - 30$.
$26+14y - 26\leq - 30 - 26$
$14y\leq - 56$

Step2: Solve for y

Divide both sides of the inequality by 14. Since 14>0, the direction of the inequality sign remains the same.
$\frac{14y}{14}\leq\frac{-56}{14}$
$y\leq - 4$

To graph the solution on the number - line:

1. Plot a closed circle at $y = - 4$ (because the inequality is $\leq$, which includes the endpoint).
2. Draw a ray to the left of $y=-4$ to represent all the values of y that satisfy the inequality.

Answer:

The solution of the inequality is $y\leq - 4$. On the number - line, there is a closed circle at $-4$ and a ray extending to the left.