Question

Which graph represents the solution to the compound inequality? 4x + 8 < –16 or 4x + 8 ≥ 4 A number line with an open circle at negative 6 with a bold line pointing to the right ending at the point at negative 1. A number line with a point at negative 6 with a bold line pointing to the right ending at the open circle at negative 1. A number line with an open circle at negative 6 with a bold line pointing to the left. A point at negative 1 with a bold line pointing to the right. A number line with a point at negative 6 with a bold line pointing to the left. An open circle at negative 1 with a bold line pointing to the right.

Answer 1

In edg:

A & B

A: StartFraction x over 2 EndFraction less than 1 or StartFraction 4 x minus 2 over 2 EndFraction greater than or equal to 13.< 1 or ≥ 13

B: 3x – 3 < 3 or 2x + 8 ≥ 22

Answer 2

a line starting at -6 going to the left of this number, and with an open circle around the -6.

Explanation:

To solve for this inequality, we need to isolate "x" on one side of the inequality symbol (<):

4 x + 8 < -16

subtract 8 from both sides:

4 x < -16 - 8

4 x < - 24

now divide both sides by 4 to get rid of the 4 that appears multiplying "x":

x < - 24/4

x < - 6

To graph this inequality one needs to highlight all the real numbers of the number line to the left of the value -6, making sure that one draws an open circle around the -6 because we don't want this number to be included (notice that x < -6 implies x-values strictly smaller than -6)

Then one would draw a line starting at -6 going to the left of this number, and with an open circle around the -6.