Question

5. –2(x – 3) ≥ 5 – (x + 3)

7. Describe a real life scenario where inequalities are used and state the inequality.

Answer 1

5 - (x + 3) ≤ -2(x - 3)
5 - x - 3 ≤ -2x + 6
5 - 3 - x ≤ -2x + 6
2 - x ≤ -2x + 6
2x - x ≤ 6 - 2
x ≤ 4

Answer 2

For real life scenarios using inequalities, it is best to think of ranges between two quantities that represent an ideal situation. For example \(37^{\circ} \le x \le 41^{\circ}\) is the ideal temperature range for food storage in a refrigerator.

Answer 3

If food is stored below 37 degrees, then freezing could occur. Above 41 degrees, and spoilage could occur.

Answer 4

Another is speed limits. On certain highways: \(40 < x < 65\) mph is the ideal speed for safe travel.

Answer 5

Thank you!

Answer 6

Could you explain how you did the inequality this this though:
"4. 2(x + 5) > 8x – 8
Distribute the 2
2x + 10 > 8x – 8
Subtract ten from both sides
2x > 8x – 18
Subtract 8x from both sides
-6x > -18
Divide by -6
x < 3"
Im a little confused on how you did it.

Answer 7

^I'm pretty sure I did not do that one. I never divide by negative

Answer 8

I know but could explain on the one you did do.

Answer 9

If I did it, I would have done this:

8x - 8 < 2x + 10
8x - 2x < 8 + 10
6x < 8 + 10
6x < 18
x < 18/6
x < 3

Answer 10

Oh, you want me to explain by including the explanations for each step?

Answer 11

Yes please

Answer 12

–2(x – 3) ≥ 5 – (x + 3)

1. Express the inequality using a less than equal sign
5 - (x + 3) ≤ -2(x - 3)

2. Distribute -1 across x + 3:
5 - x - 3 ≤ -2x + 6

3. Place like terms next to each other (associate property)
5 - 3 - x ≤ -2x + 6

4. Subtraction Property (5 - 3 = 2)
2 - x ≤ -2x + 6

Add 2x to both sides: Subtract 2 from both sides:
2x - x ≤ 6 - 2

Simplify
x ≤ 4

Answer 13

Using the less than equal sign is a matter of preference, however, it does naturally reflect placement along a number line.

For example:
x ≤ 4 means x includes 4 and all values to the left of 4: