Posted by **Julianna** on Saturday, January 31, 2009 at 1:44pm.

Right now we are learning about absolute value inequalities. I have to solve and graph this inequality:

Pretend my paranpheses are absolute value signs

(x-4) + 5 is greater than or equal to 10.

I assume I would take 5 away from each side first. But what would be the correct way to display this on a line, and what would be its set builder notation and interval notation?

Thank you so much! :-)

- Here's what I got... -
**Julianna**, Saturday, January 31, 2009 at 1:53pm
I took away 5 from each side and added 4 to each side. That got me

(x) is greater than or equal to 14.

Would this make the set builder notation be:

{x such as x is greater than or equal to 4}

And the interval notation be:

(negative infinity, 14] U [14, infinity)?

Thanks! :-)

- Algebra -
**drwls**, Saturday, January 31, 2009 at 2:08pm
You have to consider two cases. I will leave out the = sign for convenience.

(1) If x - 4 > 0, then

x - 4 + 5 > 10

x > 9 (which satisfies the x>4 assumption)

(2) If x - 4 < 0, then

If 4 - x + 5 > 10, then

-x > 1

x < -1

(which satisfies the x<4 assumption)

## Answer this Question

## Related Questions

- algebra 1 - Inequality 3 | 2x-2 | +16<58 •simplify as much as possible ...
- Algebra - Solve. Pretend the paranpheses are absolute value bars. (t-7) + 3 = 4 ...
- calculus - Let M=1000. Which of the conditions is equivalent to f(x)= 1/((4x-12...
- Algebra - I need help with solving these absolute value inequalities. I have to ...
- Math - 1. Suppose a and b are integers, and the absolute value of a is > than...
- math !!!!!!please part of a major grade!!!!!! - when in the absolute value of x ...
- algebra 2 - [=absolute value [-2x+1]>2 ok im doin inequalities and the only ...
- Algebra - 12. Determine if the following is a conjuction or disjunction. y + 4 &...
- Math - Can someone please help me with an algebra problem? -|4-8b|=12 I really ...
- math - when in the absolute value of x equal to the absolute value of negative x...

More Related Questions