Word Problems and Inequalities

[Hikari_Dreamer_12]

How do you find the measure of an angle where its supplement is 10 degrees more than its complement?

I don't want to do guess and check.
If the angle is x and the complement is 90-x would the supplement be (90-x)+10?
I tried doing x+90-x+10=180, but the x cancels out, so I have no idea what to do.
How do you do this question as well:

Find all sets of three consecutive multiples of 6 when the sum is between -6 and 70.

Thanks! I just can't seem to get word problems...
Plus, how do you do something like

{x: -4<x<6}

? There's also a question that has "|" in the place of the colon. What's the difference?

[stapel_eliz]

How do you find the measure of an angle where its supplement is 10 degrees more than its complement?

Work in steps:

The supplement and complement are defined in terms of the angle, so pick a variable to stand for the angle.

Then create an expression, in terms of that variable, to stand for the supplement.

Create another expression, again in terms of the variable, to stand for the complement.

Then create an equation for "(the supplement) is (ten more than) (the complement)".

Then solve the equation.

Find all sets of three consecutive multiples of 6 when the sum is between -6 and 70.

A "multiple of six" is a number of the form "6n". What would be an expression for the "next" "multiple of six"? What would be the next multiple after that?

What then would be the sum of the three multiples? (Simplify the polynomial expression!)

What compound inequality would indicate "(the sum) is between (-6) and (70), inclusive"?

Solve the inequality, and then create the listing of sets of multiples, working from the values of "n".

{x: -4<x<6}

Are you supposed to list out the integer members of the set? Graphing the real-number solution? Or something else?

There's also a question that has "|" in the place of the colon. What's the difference?

In my experience, there is no difference.

(Wouldn't it be nice if they picked a set-notation standard, and then stuck to it?!?)

[Hikari_Dreamer_12]

Hello again! Thanks for helping me out so many times! I definitely appreciate it!

How do you find the measure of an angle where its supplement is 10 degrees more than its complement?

Work in steps:

The supplement and complement are defined in terms of the angle, so pick a variable to stand for the angle.

Then create an expression, in terms of that variable, to stand for the supplement.

Create another expression, again in terms of the variable, to stand for the complement.

Then create an equation for "(the supplement) is (ten more than) (the complement)".

Then solve the equation.

Okay, this seemed a bit easier in the beginning, but then I came up with this:
The angle is x, the supplement angle is 90-x+10, and the complement is 90-x.
I tried this: 90-x+10=90-x
Which simplifies to 100-x=90-x
The problem with this one for me are the x's. When I move one over, that would be 0.
I still quite don't get it.

Find all sets of three consecutive multiples of 6 when the sum is between -6 and 70.

A "multiple of six" is a number of the form "6n". What would be an expression for the "next" "multiple of six"? What would be the next multiple after that?

What then would be the sum of the three multiples? (Simplify the polynomial expression!)

What compound inequality would indicate "(the sum) is between (-6) and (70), inclusive"?

Solve the inequality, and then create the listing of sets of multiples, working from the values of "n".

I got this one, thanks!

{x: -4<x<6}

Are you supposed to list out the integer members of the set? Graphing the real-number solution? Or something else?

I'm supposed to do something like this:
{x: x>8 or x<2} The answer is |x-5|>3. The problem is that I don't know how my teacher even got it!

There's also a question that has "|" in the place of the colon. What's the difference?

In my experience, there is no difference.

(Wouldn't it be nice if they picked a set-notation standard, and then stuck to it?!?)

That's one of the many things that I don't get about math!

[stapel_eliz]

The angle is x, the supplement angle is 90-x+10

What is the definition of a supplementary angle? Does your expression ("80 - x") fulfill this definition?

I'm supposed to do something like this:
{x: x>8 or x<2} The answer is |x-5|>3.

Were the instructions something like "express as an absolute-value inequality"...? If so, then try here to learn how that works.

[Hikari_Dreamer_12]

The angle is x, the supplement angle is 90-x+10

What is the definition of a supplementary angle? Does your expression ("80 - x") fulfill this definition?

Um, what do you mean by 80-x? Is it the supplementary angle of the 90-x+10 one?

I'm supposed to do something like this:
{x: x>8 or x<2} The answer is |x-5|>3.

Were the instructions something like "express as an absolute-value inequality"...? If so, then try here to learn how that works.

[/quote]

The instructions were Write an equation or inequality involving absolute value whose solution set is given. Isn't that the same?

[stapel_eliz]

Um, what do you mean by 80-x?

Sorry; I'd transposed the "minus" sign. You've provided an expression which simplifies to "100 - x". But what is the definition of a supplementary angle? So what expression would stand for "supplement of x"?

The instructions were Write an equation or inequality involving absolute value whose solution set is given. Isn't that the same?

Yes. (I don't see that the instructions were posted before.)

[Hikari_Dreamer_12]

Um, what do you mean by 80-x?

Sorry; I'd transposed the "minus" sign. You've provided an expression which simplifies to "100 - x". But what is the definition of a supplementary angle? So what expression would stand for "supplement of x"?

Oh. So you mean 100-x=180-x? But what about the x? If this is correct, then wouldn't the x equal zero once you move them to the same side?

The instructions were Write an equation or inequality involving absolute value whose solution set is given. Isn't that the same?

Yes. (I don't see that the instructions were posted before.)

Sorry about that, I forgot to post the instructions. Thanks!

[stapel_eliz]

You're trying to go straight from the variable to the equation. Instead, try working in steps:

Work in steps:

The supplement and complement are defined in terms of the angle, so pick a variable to stand for the angle.

Then create an expression, in terms of that variable, to stand for the supplement.

Create another expression, again in terms of the variable, to stand for the complement.

Then create an equation for "(the supplement) is (ten more than) (the complement)".

Then solve the equation.