## Which number line represents the solution set for the inequality –(1/2)x ≥ 4?

Question

Which number line represents the solution set for the inequality –(1/2)x ≥ 4?

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2 weeks 2021-11-21T14:14:46+00:00 2 Answers 0

1. When the sign is ≤ or ≥ (less/greater than or equal to), the dot is filled in.

When the sign is < or >, the dot is not filled in and looks like this o

To find out which number line represents the solution set, simplify the inequality and isolate x

Multiply -2 on both sides to get rid of -1/2

x ≤ -8       (The sign flips when you multiply/divide a negative number on both sides of the inequality)

so you get x is greater than or equal to -8, so you have a filled in circle on -8, and the arrow should be going to the right since x is greater than -8

2. answer : second choice / b

we have

-1/2x >_ 4

Solve the inequality

Multiply by both sides—–> remember change inequality sign

x<_ -4(2)

x<_ -8

the solution is the interval———–> (-∞,-8]

using a graph tool

see the attached figure

the solution is the shaded area: