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

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

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

Start with the given inequality

Break up the absolute value (remember, if you have , then or )

or Break up the absolute value inequality using the given rule

Now lets focus on the first inequality

Start with the given inequality

Add 3 to both sides

Combine like terms on the right side

Divide both sides by 4 to isolate x

Reduce

Now lets focus on the second inequality

Start with the given inequality

Add 3 to both sides

Combine like terms on the right side

Divide both sides by 4 to isolate x

Divide

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

Answer:

So our answer is

or

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) (Show Source): You can put this solution on YOUR website!
means that or , so:

Solve: → →

OR

Solve: → → (remember to reverse the sense of the inequality when multiplying both sides by a number less than zero) →

Therefore any number that is either less than or greater than is in the solution set of . In set builder notation:

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

RELATED QUESTIONS
What is the solution set of... (answered by Simnepi)
what is the solution set of... (answered by Fombitz)
What is the solution set of |4x � 3|+ 2 > 11? (answered by lynnlo)
A partial solution set is given. Find the complete solution set.... (answered by stanbon)
find the solution set of the equation {{{(4x-2y)/3 + (2x-3y)/5 =... (answered by kietra)
What is the solution set of |x + 3| � 2 =... (answered by ankor@dixie-net.com)
What is the solution set of | x - 5 | =... (answered by MathLover1)
what is the solution set to 4x + 5 = 2x +... (answered by jim_thompson5910)
What is the solution set of log(8x^3)-log(4x)>=logx... (answered by nerdybill)