SOLUTION: The solution set of [4x-3]>5 is_____

Algebra ->  Absolute-value -> SOLUTION: The solution set of [4x-3]>5 is_____       Log On


   

Question 174309: The solution set of [4x-3]>5 is_____
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

abs%284x-3%29%3E5 Start with the given inequality


Break up the absolute value (remember, if you have abs%28x%29%3E+a, then x+%3C+-a or x+%3E+a)

4x-3+%3C+-5 or 4x-3+%3E+5 Break up the absolute value inequality using the given rule




Now lets focus on the first inequality 4x-3+%3C+-5


4x-3%3C-5 Start with the given inequality


4x%3C-5%2B3Add 3 to both sides


4x%3C-2 Combine like terms on the right side


x%3C%28-2%29%2F%284%29 Divide both sides by 4 to isolate x



x%3C-1%2F2 Reduce


Now lets focus on the second inequality 4x-3+%3E+5


4x-3%3E5 Start with the given inequality


4x%3E5%2B3Add 3 to both sides


4x%3E8 Combine like terms on the right side


x%3E%288%29%2F%284%29 Divide both sides by 4 to isolate x



x%3E2 Divide



----------------------------------------------------

Answer:

So our answer is

x+%3C+-1%2F2 or x+%3E+2


which looks like this in interval notation





if you wanted to graph the solution set on a number line, you would get

Graph of the solution set in blue and the excluded values represented by open circles

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
abs%284x-3%29%3E5 means that 4x-3%3E5 or -%284x-3%29%3E5, so:


Solve: 4x-3%3E5 → 4x%3E8 → x%3E2


OR

Solve: -%284x-3%29%3E5 → -4x%2B3%3E5 → -4x%3E2 (remember to reverse the sense of the inequality when multiplying both sides by a number less than zero) → x%3C1%2F2

Therefore any number that is either less than 1%2F2 or greater than 2 is in the solution set of abs%284x-3%29%3E5. In set builder notation:

{All x | x is real and (x < ½ or x > 2)}