Question 1151628
{{{3(11x+14)+7 > 19+3x}}}

{{{33x+42+7 > 19+3x}}}

{{{33x-3x > 19-42-7}}}

{{{30x > -30}}}

{{{x > -1}}}

so, solution is: all {{{x}}} element of {{{R}}} greater then {{{-1}}} to {{{infinity}}}=> means {{{-1}}} is {{{not}}} included and you cannot use [{{{-1}}},{{{infinity}}})

 

so, interval is ({{{-1}}},{{{infinity}}})

number line:

<a href="https://ibb.co/PD27VHk"><img src="https://i.ibb.co/PD27VHk/MSP76.gif" alt="MSP76" border="0"></a>


In "Interval Notation" we just write the beginning and ending numbers of the interval, and use:

[ ] a square bracket when we want to include the end value, or
( ) a round bracket when we don't

Example: (5, 12]
Means from 5 to 12, do not include 5, but do include 12

The terms "Open" and "Closed" are sometimes used when the end value is included or not:

(a, b)	 	a < x < b	 	an open interval
[a, b)	 	a ≤ x < b	 	closed on left, open on right
(a, b]	 	a < x ≤ b	 	open on left, closed on right
[a, b]	 	a ≤ x ≤ b	 	a closed interval

These are intervals of finite length. We also have intervals of infinite length

We often use Infinity in interval notation.

Infinity is not a real number, in this case it just means "continuing on ..."

Example: x greater than, or equal to, 3:
[3, +∞)

There are 4 possible "infinite ends":

Interval	 	Inequality	 	 
(a, +∞)	 	x > a	 	"greater than a"
[a, +∞)	 	x ≥ a	 	"greater than or equal to a"
(-∞, a)	 	x < a	 	"less than a"
(-∞, a]	 	x ≤ a	 	"less than or equal to a"
We could even show no limits by using this notation: (-∞, +∞)