Question

1. graph the solutions to ( p > -2 ) on the number line.

1. for parts (a) and (b), consider the numbers 0, 4, 7, 9, 13, 24, 28, and 36.

a. which of the numbers are solutions to ( y + 5 > 14 )?
b. which of the numbers are solutions to ( 3.5w < 7.6 )?

Explanation:

Step1: Graph $p > -2$ on number line

1. Locate $-2$ on the number line.
2. Draw an open circle at $-2$ (since $p$ cannot equal $-2$).
3. Draw an arrow pointing to the right from the open circle (to represent all numbers greater than $-2$).

Step2: Solve $y + 5 > 14$ for $y$

$y + 5 > 14$
$y > 14 - 5$
$y > 9$
Now select numbers from $\{0, 4, 7, 9, 13, 24, 28, 36\}$ that are greater than 9: $13, 24, 28, 36$

Step3: Solve $3.5w < 7.6$ for $w$

$3.5w < 7.6$
$w < \frac{7.6}{3.5}$
$w < 2.171...$
Now select numbers from $\{0, 4, 7, 9, 13, 24, 28, 36\}$ that are less than $2.171...$: $0$

Answer:

1. (Graph description: Open circle at $-2$ on the number line, with an arrow pointing to the right towards positive infinity)
2. a. $13, 24, 28, 36$

b. $0$