5(5x+1)<4(5x+3) Solve the inequality.?

Question

Describe the solution set as an inequality in interval notation. Someone please explain how it's done don't just give me an answer

 

 

Answer 1

The inequality is 5(5x + 1) < 4(5x + 3).

(25x + 5) < (20x + 12)

25x - 20x < 12 - 5

5x < 7

x <7/5.

The solution set is {x | x < 7/5}.

Interval notation :

An interval is a connected subset of numbers.  Interval notation is an alternative to expressing the solution as an inequality.  Unless specified otherwise, we will be working with real numbers.

• When using interval notation, the symbol : ( means "not included" or "open".

                                                                   [ means "included" or "closed".

• Open Interval : (a, b)  is interpreted as a < x < b  where the endpoints are NOT included.
• Closed Interval : [a, b]  is interpreted as a < x < b  where the endpoints are included
• Half-Open Interval : (a, b]  is interpreted as a < x < b  where a is not included, but b is included.
• Half-Open Interval : [a, b) is interpreted as a < x < b where a is included, but b is not included.
• Non-ending Interval : ( a, ∞) is interpreted as x > a where a is not included and infinity is always expressed as being "open" (not included).
• Non-ending Interval :( - ∞, b] is interpreted as x < b where b is included and again, infinity is always expressed as being "open" (not included).

So, the soltution of the inequality in the interval notation is (- ∞, 7/5).