Question 1094165: could you please help me solve this equation
|5x-2|<9
I tried but my answer was not correct Found 3 solutions by jim_thompson5910, ikleyn, greenestamps:Answer by jim_thompson5910(35256) (Show Source):
|5x-2| < 9.
Divide both sides by 5. You will get an equivalent inequality
< .
The solution set to this inequality is the set of those x that are remoted less than from the point on the number line, i.e
the set of x, < x < , or, which is the same,
< x < .
Answer. The solution set is the interval (,) of the number line.
When you first learn how to solve inequalities, the way you are taught to interpret your example
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.
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
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
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.
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
the first step is to divide by 5 to get
(