1 Answer

Romanski · Answer 1 · 2021-03-14T00:23:08+0000

Answer:

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
$0\le x<2$

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