# Math Help - Absolute Value Notation/Inequality and Interval Notation

1. ## Absolute Value Notation/Inequality and Interval Notation

The distance between x and 5 is 3, what is the solution to this and notation?

The distance between -4 and x is 7, what is the solution to this and notation?

The distance between x and a is b, what is the solution to this and notation?

Use both inequality and interval notation to describe the following sets.

a) z is at least 10

Find inequality and interval

b) y is no more than 25

Find inequality and interval

Thanks, this is for Algebra 2 Honors and was just having some problems with these.

2. Originally Posted by bherrell2
The distance between x and 5 is 3, what is the solution to this and notation?
Since you title this "Absolute Value Notation/Inequality", I would think that you know that the distance between points p and q, on the real line, is |p- q|. The distance between x and 5 is 3 so |x- 5|= 3. So either x- 5= 3, which gives x= 5+ 3= 8 or -(x- 5)= 3 so x- 5= -3 and x= 5- 3= 2. You could also answer that by marking 5 on a number line and counting off 3 space right and left.

The distance between -4 and x is 7, what is the solution to this and notation?

The distance between x and a is b, what is the solution to this and notation?
Why don't you try the second problem now yourself? "The distance between x and a is b" gives |x- a|= b so either x-a= b or -(x-a)= b. Solve those for b.

Use both inequality and interval notation to describe the following sets.

a) z is at least 10
$z\ge 10$ which is the interval $\left[10, \infty\right)$

Find inequality and interval

b) y is no more than 25

Find inequality and interval

Thanks, this is for Algebra 2 Honors and was just having some problems with these.