Question 1094165
<br>Not a new solution; but rather a note to the student about the two responses you got.<br>
When you first learn how to solve inequalities, the way you are taught to interpret your example
{{{abs(5x-2)<9}}}
is to say that the value of the expression 5x-2 is between -9 and 9.  The first response you got to your question solved the inequality that way.<br>
For many applications where absolute values are encountered, the method used in the second response nearly always is easier to understand and to work with.  The idea behind that method is that the inequality
{{{abs(x-a)<d}}}
means x is any value such that the distance between x and some fixed point a is less than some fixed distance d.  For example, you could solve the inequality
{{{abs(x-7)<=3}}}
algebraically and get the answer 4 <= x <= 10; but the easier way to that answer is to think of all the numbers whose distance from 7 is less than or equal to 3.  3 either direction from 7 gets you to 4 and 10, so the solution set is every number between 4 and 10.<br>
So for all but elementary problems involving absolute values, understanding the second solution method will make your work easier.  Note that in the second solution, her first step was to divide the whole inequality to get it in the required form, with a coefficient of 1 on the "x" in the absolute value symbol.  That is, where the original inequality was
{{{abs(5x-2)<9}}}
the first step is to divide by 5 to get
{{{abs(x-2/5)<9/5}}}