Answer:
-6≤q≤-10
Step-by-step explanation:
Given the inequality |q+8|≥2, we are to solve for q. Note that the function inside modulus sign will return both negative and positive value.
For the positive function:
q+8≥2
Subtract 8 from both sides of the inequality.
q+8-8≥2-8
q ≥ -6
For the negative function;
-(q+8)≥2
open the parenthesis
-q-8≥2
add 8 to both sides
-q-8+8≥2+8
-q≥10
Multiply both sides by -1. Note that multiplying both sides of an inequality changes the direction of the inequality sign.
q≤-10
Combining both results i.e q ≥ -6 and q≤-10
q ≥ -6 can also be written as -6≤q
Combining -6≤q with q≤-10, this will give -6≤q≤-10.
Hence the result of the inequality function given is -6≤q≤-10.
