We are given two problems. (a) We are given a number line with a filled circle at -3 and an arrow pointing to the right. We need to write the inequality in $x$ that this diagram represents. (b) We are given a shaded region on the $xy$-plane. We need to write the inequality in $x$ that this diagram represents. (c) We are given an inequality $20 + 7x \le 34$ and need to solve for $x$.

1. Problem Description

We are given two problems.

(a) We are given a number line with a filled circle at -3 and an arrow pointing to the right. We need to write the inequality in $x$ that this diagram represents.

(b) We are given a shaded region on the $xy$-plane. We need to write the inequality in $x$ that this diagram represents.

(c) We are given an inequality $20 + 7x \le 34$ and need to solve for $x$.

2. Solution Steps

(a) The filled circle at -3 means that -3 is included in the solution. The arrow pointing to the right means that all values greater than -3 are also included.

Therefore, the inequality is $x \ge -3$.

(b) The shaded region is to the left of the vertical line $x=1$. Therefore, the inequality is $x \le 1$.

(c) We are given the inequality $20 + 7x \le 34$.

Subtract 20 from both sides:

$7x \le 34 - 20$

$7x \le 14$

Divide both sides by 7:

$x \le \frac{14}{7}$

$x \le 2$

3. Final Answer

(a) $x \ge -3$

(b) $x \le 1$

(c) $x \le 2$