Question

Help please ASAP!!! Quick

Answer 1

6.
`15x-125\ge 205,\ \ \ 22\ hours`

7.
`0\le x<2`

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

`\$(15x-125)`

This amount must be at least $205, so

`15x-125\ge 205`

Solve this inequality:

`15x-125+125\ge 205+125\\ \\15x\ge 330\\ \\x\ge 22`

Hence, the fewest number of hours she works in a week is 22 hours.

7. Solve the inequality

`|2x-1|<3`

Rewrite it as a double equivalent inequality:

`-3<2x-1<3`

Add 1:

`-3+1<2x-1+1<3+1\\ \\-2<2x<4`

Divide it by 2:

`-1<x<2`

Non-negative integer solutions are
`0\le x<2`