Question

write a compound inequality that represents each phrase. graph the solution.

1. all real numbers that are less than −3 or greater than or equal to 5 x < -3 or x ≥5

hand - drawn number line

1. the time a cake must bake is between 25 minutes and 30 minutes, inclusive.

solve each compound inequality. graph your solution.

1. 5 < k − 2 < 11

hand - drawn work and number line

1. −4 > y + 2 > −10

Explanation:

Problem 2:

Step1: Define the variable

Let \( t \) represent the baking time of the cake (in minutes).

Step2: Translate the phrase to inequality

The time is between 25 and 30 minutes, inclusive. So, \( 25 \leq t \leq 30 \).

Step1: Add 2 to all parts

To solve \( 5 < k - 2 < 11 \), we add 2 to each part of the compound inequality.
\( 5 + 2 < k - 2 + 2 < 11 + 2 \)

Step2: Simplify each part

Simplifying the left, middle, and right parts:
\( 7 < k < 13 \)

Step1: Subtract 2 from all parts

To solve \( - 4>y + 2>-10 \), we subtract 2 from each part of the compound inequality.
\( - 4-2>y + 2 - 2>-10 - 2 \)

Step2: Simplify each part

Simplifying the left, middle, and right parts:
\( - 6>y>-12 \) or we can write it as \( - 12 < y < - 6 \)

Answer:

The compound inequality is \( 25 \leq t \leq 30 \), where \( t \) is the baking time (in minutes). For the graph, we draw a number line, mark 25 and 30 with closed circles (since the inequality is inclusive), and shade the region between them.

Problem 3: