X2 < 10 what are the inequalities?. Are You guys own this kind of concern?, If do then please check the good tips below this line:\r\n
Solving linear inequalities is almost exactly like solving linear equations.
Solve x + 3 < 0.
If they`d given me "x + 3 = 0", I`d have known how to solve: I would have subtracted 3 from both sides. I can do the same thing here:
Then the solution is:
x < –3
"Set notation" writes the solution as a set of points. The above solution would be written in set notation as "x ", which is pronounced as "the set of all x-values, such that x is a real number, and x is less than minus three". The simpler form of this notation would be something like " x
< –3", which is pronounced as "all x such that x is less than minus three".
"Interval notation" writes the solution as an interval (that is, as a section or length along the number line). The above solution, "x < –3", would be written as "", which is pronounced as "the interval from negative infinity to minus three", or just "minus infinity to minus three". Interval notation is easier to write than to pronounce, because of the ambiguity regarding whether or not the endpoints are included in the interval. (To denote, for instance, "x < –3", the interval would be written "", which would be pronounced as "minus infinity through (not just "to") minus three" or "minus infinity to minus three, inclusive", meaning that –3 would be included. The right-parenthesis in the "x < –3" case indicated that the –3 was not included; the right-bracket in the "x < –3" case indicates that it is.)
The last "notation" is more of an illustration. You may be directed to "graph" the solution. This means that you would draw the number line, and then highlight the portion that is included in the solution. First, you would mark off the edge of the solution interval, in this case being –3. Since –3 is not included in the solution (this is a "less than", remember, not a "less than or equal to"), you would mark this point with an open dot or with an open parenthesis pointing in the direction of the rest of the solution interval:
Inequalities crop up frequently in math and science. You may be familiar with plotting these on a number line using open and closed circles to represent strict inequality and "or-equal-to" inequalities, or you may be new to plotting inequalities on a number line altogether. No matter the convention used (circle or brackets and parentheses), it displays a set of values a variable can take on while obeying an inequality.
1.Mark all strict inequalities with parenthesis, using the appropriate parenthesis. All "greater than" inequalities should be marked with a left parenthesis, and all "less than" inequalities with a right parenthesis. For example, mark "x > 3" with "(" at 3, and mark "x < 5" with ")" at 5.
2.Mark all "or-equal-to" inequalities with square brackets, using the appropriate bracket. All "greater-than-or-equal-to" inequalities should be marked with a left bracket and all "less-than-or-equal-to" inequalities with a right bracket. For example, mark "x >= 4" with "[" at 4, and mark "x <= 1" with "]" at 1.
3.Embolden the region of the number line between the highest left bracket or parenthesis and the lowest right bracket or parenthesis. Many inequalities describe a variable as being both greater than one number and less than another as in "4 < x <= 8," and emboldening the region between the "(" at 4 and the "]" at 8 indicates that x may be anywhere in that region. If only one bound is provided, like "x > 4," then embolden until the end of the number line.
Have a Great Day.