Question

what is an inequality, why would I use it or try to solve it. I just found out that an exponet is not a number it is an abbreviation, so is an inequality something of the same kind of process

Answer 1

An inequality gives bounds on some expression. An equality gives an exact solution.

x = 4 means x is 4.
\(x \le 4\) means x can be at most 4.

Answer 2

Does that make sense?

Answer 3

So if someone tells you something like:

Let w be the weight of a package. And the weight of a package is always between 2 and 5 pounds. You can translate that into an inequality:
\[2\le w \le 5\]

Answer 4

So far yes and you are the first person/now super hero to say such a good answer with awesome insight. Next, How would I know if a value is a solution for an inequality and inequality sign change when both sides are multiplied or divided by a negative. Why can't the textbook just tell us?

Answer 5

Ok so a value is a solution to an inequality if it makes the inequality true.

Answer 6

For example, which of the following are solutions to the inequality \(2 \le w \le 5\):

1, 2.5, 4, 7, -3

Answer 7

the wieght example makes sense completely.

Answer 8

2.4 and 4

Answer 9

2.5, but yes.

Answer 10

Correct

Answer 11

You always change the direction of inequalities if you multiply or divide by a negative.

Answer 12

Though I avoid this by adding/subtracting instead.

Answer 13

Ok , so this is a rule for inequalities but what about in equations

Answer 14

For example, lets say you had the inequality:

\[1-w < 3\]

You can subtract a 1 from both sides to get:
\[-w < 2\]

Then multiply both sides by -1 to get:
\[w > -2\]

Answer 15

Notice the direction changed.

Answer 16

You don't have to worry about equalities because the equal sign is exact. It's not a range, so it doesn't have a direction.

Answer 17

So we find that any w greater than -2 will be solutions to the original inequality (or any of the intermediate steps)

Answer 18

For example, 3 is greater than -2, so if we plug in 3 for the original:

\[1-3 \lt 3\]

We get -2 < 3 which is true.

Answer 19

But if we pick a w that's not greater than -2 (say -4 for example)

\[1-(-4) < 3\]

We get 5 < 3 which is false. So -4 does not satisfy this inequality.

Answer 20

If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality?



yes, I see it changed is that because the bounds are now set to be anything higher than -1

Answer 21

Only if the inequality is one of \[\le or \ge\]

Because those inequalities allow for the possibility of it being equal.

Answer 22

If it's strictly < or > then it cannot be =

Answer 23

Any other questions?

Answer 24

how did you know to write the expression -1(-4) ? 3 and why is is it a -5

Answer 25

my computer will let me type a couple letters every few seconds

Answer 26

9*6+3< 9*4
Yipee, this would be my first inequality

Answer 27

Ok, well that one is just true or false.

Answer 28

is 9*6 + 3 less than 9*4?

Answer 29

Sometimes this site gets a bit laggy if the question-thread gets too long (like this one is). Perhaps we can continue this in a different question-thread.