Evaluate the Function, Set Builder Notation...

[Blue Leader]

Greetings,

I'm having some problems, obviously, with some of my math work. There's a few different ones so hopefully this will all make sense...
Any help would be appreciated.

1. Evaluate the function for the given values:
\(\displaystyle f(x) = 5 -3x; x = -4, 2\)
I'm not sure where to go with that one. I'd assume I'd combine like terms (5+4=9, x+3x=4x), though I'm not sure what to do after that. Nor am I sure what to do with the ", 2".

2. Solve:
\(\displaystyle \frac{k+1}{3} - \frac{1}{2} = \frac{3k-3}{6}\)
Again, I'm not really sure where to go with this. I've always struggled greatly with fractions...

3. Solve and list the answer in Set Builder Notation:
\(\displaystyle 4x - 6 > 12 - 10x\)
For this one I've got the equation down to...
\(\displaystyle 6 > -14x\)
But I'm not sure what to do from there...

And one last question... I've got a problem similar to number 3, however instead of it saying to list the answer in Set Builder Notation it just says to list it graphically. How would I list it graphically? I'm not entirely sure what it's asking me to do.
The problem is almost identical to number 3, just different numbers.

Thank you for your time and for your help!

 

[masters]

Greetings,

I'm having some problems, obviously, with some of my math work. There's a few different ones so hopefully this will all make sense...
Any help would be appreciated.

1. Evaluate the function for the given values:
\(\displaystyle f(x) = 5 -3x; x = -4, 2\)
I'm not sure where to go with that one. I'd assume I'd combine like terms (5+4=9, x+3x=4x), though I'm not sure what to do after that. Nor am I sure what to do with the ", 2".

2. Solve:
\(\displaystyle \frac{k+1}{3} - \frac{1}{2} = \frac{3k-3}{6}\)
Again, I'm not really sure where to go with this. I've always struggled greatly with fractions...

3. Solve and list the answer in Set Builder Notation:
\(\displaystyle 4x - 6 > 12 - 10x\)
For this one I've got the equation down to...
\(\displaystyle 6 > -14x\)
But I'm not sure what to do from there...

And one last question... I've got a problem similar to number 3, however instead of it saying to list the answer in Set Builder Notation it just says to list it graphically. How would I list it graphically? I'm not entirely sure what it's asking me to do.
The problem is almost identical to number 3, just different numbers.

Thank you for your time and for your help!

Hi Blue Leader,

1. Evaluate the function for the given values.

I believe all you need to do here is take the separate values you are given for x and substitute them into your given function.

\(\displaystyle f(x)=5-3x\)

\(\displaystyle f(-4)=5-3(-4)=\)

\(\displaystyle f(2)=5-3(2)=\)

2. Solve \(\displaystyle \frac{k+1}{3}-\frac{1}{2}=\frac{3k-3}{6}\)

Multiply each term by the LCD, which is 6.

\(\displaystyle 2(k+1)-3=3k-3\)

Now, you should be able to solve for k

3. \(\displaystyle 4x-6>12-10x\)

Add 10x to both sides, then add 6 to both sides

\(\displaystyle 14x>18\)

Divide both sides by 14 and reduce the fraction.

\(\displaystyle x>\frac{9}{7}\)

The answer in set builder notation would look like this: \(\displaystyle \left\{x|x>\frac{9}{7}\right\}\), which is read "the set of all x, such that x is greater than 9/7.

To state the solution graphically, draw a number line and indicate where 9/7 would be. Put an open circle around that location and shade all points to the right using an arrowhead to indicate positive infinity. The open circle on the 9/7 location indicates that 9/7 is not part of the solution.

<---------0-----9/7===========>

 

[Blue Leader]

Ah, thank you very much.