Answer:
6. [tex]15x-125\ge 205,\ \ \ 22\ hours[/tex]
7. [tex]0\le x<2[/tex]
Step-by-step explanation:
6. Let x be the number of hours Manuela works in a week. She makes $15 per hour, so $15x is the amount of money she earns in a week.
$125 should be deducted, so she is left with
[tex]\$(15x-125)[/tex]
This amount must be at least $205, so
[tex]15x-125\ge 205[/tex]
Solve this inequality:
[tex]15x-125+125\ge 205+125\\ \\15x\ge 330\\ \\x\ge 22[/tex]
Hence, the fewest number of hours she works in a week is 22 hours.
7. Solve the inequality
[tex]|2x-1|<3[/tex]
Rewrite it as a double equivalent inequality:
[tex]-3<2x-1<3[/tex]
Add 1:
[tex]-3+1<2x-1+1<3+1\\ \\-2<2x<4[/tex]
Divide it by 2:
[tex]-1<x<2[/tex]
Non-negative integer solutions are [tex]0\le x<2[/tex]
