Question

Joanne's ideal weight is 140 pounds. The number of pounds she actually weights (w) usually varies no more than 10 pounds from this ideal weight. Which inequality below represents this scenario?

|w + 140| greater than or equal to 10

|w - 140| less than or greater to 10

|w - 10| less than or greater to 140

|w + 10| greater than or equal to 140

Answer 1

do u know it

Answer 2

when you say less than or greater to do you mean less than or equal to as in \[x \le 10 \]

Answer 3

so it says in the question is no more than 10 so it must be less than or euqal to ten since it cannot be more

Answer 4

yes

Answer 5

that gives you the sign of the equality

Answer 6

so its either b or c

Answer 7

ok since it has to be less than or equal to ten try pluggin weights that would be different but within that range like 135 or 142

Answer 8

yes either b or c

Answer 9

c right

Answer 10

you got it

Answer 11

Select the inequality that corresponds to the given graph.

number line with an open circle on negative 3, shading to the left and an open circle on 2, shading to the right

|2x - 4| > 2

|4x + 2| > 10

|4x - 6| less than or greater to 14

|6x + 4| less than or greater to 16

Answer 12

Since the weight varies by no more than 10 lb, then the weight can be from 130 to 150 lb.

That means

\(w \ge 130 \) and \(w \le 150\)

which can be written as

\(130 \le w \) and \(w \le 150\)

or

\(130 \le w \le 150 \)

Subtract 140 from all three "sides" to get:

\(-10 \le w-140 \le 10 \)

This corresponds to the absolute value inequality:

\(|w - 140| \le 10\)

This makes sense because this absolute value inequality can be interporeted as "the difference between the weigtht and 140 lb is less than or equal to 10."

Answer 13

so c right

Answer 14

@jpw @recon14193
The answer to the first question is B, not C.

Answer 15

good i would have never seen that

Answer 16

If you want to show C is not the answer, notice that w = 0 is a solution to C, but according to the problem the person can weigh from 130 lb to 150 lb, not 0 lb.

Answer 17

can u help me with the other one

Answer 18

Also, when you copy problems, be careful with the expressions "greater than or EQUAL to" and "less than or EQUAL to." For choices B and C you wrote "leess than or GREATER TO" which makes no sense.

Answer 19

Yes, I'll help.

Answer 20

Select the inequality that corresponds to the given graph.

number line with an open circle on negative 3, shading to the left and an open circle on 2, shading to the right

|2x - 4| > 2

|4x + 2| > 10

|4x - 6| less than or greater to 14

|6x + 4| less than or greater to 16

Answer 21

the equal to sorry

Answer 22

Got it.
For the second problem. Since the solution has open circles, that tells you something already.
An open circle comes from < or >.
A closed circle comes from \(\le\) or \(\ge\).
That means you can eliminate choices C and D.

Answer 23

is it a

Answer 24

Now we can solve each inequality in choices A and B, and see which one gives the result you have.

|2x - 4| > 2

To solve an absolute value inequality of the type above,
|X| > k
where X = expression in x, and k = number, just change the absolute value equation into the follwoing compound inequality:

X > k or X < -k

With our problem, the absolute value inequality becomes:

2x - 4 > 2 or 2x - 4 < -2

Now we need to solve each inequality and use the word "or" in between them.

2x > 6 or 2x < 2
x > 3 or x < 1
There is no -3 and 2 here, so it can't be A.

Now let's try B.

Answer 25

We use the same method for

|4x + 2| > 10

turning it into:

4x + 2 > 10 or 4x + 2 < -10

4x > 8 or 4x < -12

x > 2 or x < -3

Since we have < and >, that means open circles.
The answer is the number line below.