Question

Determine the value that is a solution to the inequality. *
5x - 8 ≥ 22
6
5
4
3

Answer 1

I know I would do +8 to both sides. So 5 + 8 = 13
22+ 8 = 30
-8 + 8 = 0
@tkhunny

Answer 2

Why did you pick "+8" for starters?

Answer 3

I figured 8 was negative and we want to cancel that out so I did +8

Answer 4

That is good. What does that leave?

Answer 5

5x >_ 22

Answer 6

But I would add 8 to both sides. so 13 >_ 30?

Answer 7

What happened to "5x"? We've done nothing with that. Just stik with modifying LIKE terms.

\(5x - 8 ≥ 22\)

\(5x - 8 + 8 ≥ 22 + 8\)

\(5x + 0 ≥ 30\)

\(5x ≥ 30\)

You cannot combine constants with variable terms in that manner.

Answer 8

oh. But how would one determine a value that is a solution to an equality? Inequalities aren't problems like 1+1.

Answer 9

Why is that confusing? It leads to a comprehensible result or it doesn't

If you substitute x = 4, and conclude that \(5(4) = 20 \ge 30\), then something is very wrong. Answers tend to be in intervals, not single values.

Answer 10

Oh, that makes much more sense. So 5 would be the answer?

Answer 11

Divide my last expression by 5 and see. Your answer will be an INTERVAL, not a single value. There are infinitely many values that work just fine.

Answer 12

True, So all of these numbers above are correct then?

Answer 13

No. Why would you say that? Try them in the inequality and see if they work.

We had \(5x \ge 30\)

Dividing by 5

We have \(x \ge 6\)

Which of the values is/are AT LEAST 6?

Answer 14

I might type something very unrelated to it but it is related in a way.
6 / 2 = 3.? Anyway At least 6? What do you mean.

Answer 15

Ok from what I'm getting. divide 30 by 5 and we get 6. We want to try the numbers in the inequality. But what do you mean by Which of the values are at least 6?

Answer 16

That's what inequalities are all about.

\(x \ge 6\) can be read a couple ways.

"x is greater than or equal to 6"

"x is at least 6"

Notice what works and what doesn't.

"4 is NOT greater than or equal to 6"
"2 is NOT greater than or equal to 6"
"7 is greater than or equal to 6"
"8 is greater than or equal to 6"

"4 is NOT at least 6"
"2 is NOT at least 6"
"7 is at least 6"
"8 is at least 6"

Answer 17

OH this sign ≥
means that the inequality or X is greater than 6, or equal to, but never less than 6. The sign backwards would mean the inequality is at least six, but not any higher, just less.

Answer 18

No.

\(x \ge 6\) means x is AT LEAST 6.
\(x \le 6\) means x is AT MOST 6.

Answer 19

≤ 4 = The inequality is at most 4
≥ 4 = The inequality is at least 4.
Basically?
The answer would be 6 then. 5, 4, and 3 are all less than 6.

Answer 20

That's it. :-)