When are inequalities better than equations?
966956
They are better when finding answers to a question with possibly more than one right answer. For example, solve for x: 5x=15 would be best with an equation because it's easily solvable with one answer. Whereas, A number greater than 9 but less than 12 would be set up as 9<x<12 or 9<x & x<12.  This way, x could be any number between 9 and 12, having infinate solutions. If you have to see how much money you can spend with out going over the allotted amount, would be a real world situation. (IE- You have 20 dollars to spend, and you can't spend negative dollars, so 0<x<20). There you go!
1163625
Improper fractions are much easier to deal with in any math, physics, or chemistry equation than mixed numbers.\n\nThe only time mixed numbers are easier are for graphing purposes or in explaining your results to someone without a math background (which, sadly, is most everybody that doesn't post here).\n\n;-)
749096
Solve the inequality the same way you would any other equation. Just remember that when dividing or multiplying by a negative number you have to flip the inequality.
780452
Solve it just like a regular equality:\n\nx-6 ≤ 7\n\nAdd 6 to both sides, to get:\n\nx ≤ 13  ← this is your answer\n\nWhen working with inequalities, you can add and subtract from both sides just as you would in a regular equality.  You can also multiply and divide both sides, but the trick to keep in mind is that if you multiply or divide by a negative number, you need to change the sign!  For example, if you had:\n\n-2x ≤ 10\n\nDivide both sides by -2 AND REVERSE THE INEQUALITY to get:\n\nx ≥ -5\n\nHope that helped!\n\n~ ♥ ~\n\nEDITED TO ADD:  A "regular equality" would be where you have an equal sign rather than a < or > sign.  So x-6 = 7 is an equality.\n\nGood luck kid ... sounds like you will need it!
767112
Here's what you should think: 3 times a number that has to be zero or higher, then having another 3 added to it, cannot possibly equal 1 (it must be at least 3).  So there is no solution.\n\nYou did say it was an inequality, though.  If the = was really > or >=, the answer is all real numbers.  If it was < or <= the answer is the empty set.
787480
if x is positive, then I x I is always equal to the value, but not less than it.\nif x is negative, then I x I will be a positive value which is never less than a negative value.\nso, the inequality holds good only for positive values of x.
403670
If for some reason you are having trouble with this, draw a number line, write down where 9 and -4.72 are on it, and see whether it makes sense that the inequality is or is not satisfied.
363348
Are we solving for x?
434590
because in more complex fields of mathematics, equations are as yet unsolvable, and the best we can do is make approximations. in fact there is an entire field of math devoted to this.
471125
Hi!\nI'm suprised nobody used the easiest way that i will demonstrate now.\n\nLets assume further that x is positive real.\n\nWe start with a simple fact that ANY squares are nonnegative. The idea is we "choose" a square intelligently to suit our purpose. Also not that x does NOT equal zero.\n\nBy experience, \nI choose the square ( x^(1/2) - 1 / [ x^(1/2)] )^2.\nIt must be nonnegative for whatever positive real values of x.\nThus,\n\n    ( x^(1/2) - 1 / [ x^(1/2)] )^2 >= 0\n\nExpanding and regrouping, we get,\n\n    x - 2 + 1/x >= 0 \n      \nor equivalently,\n\n      x + 1/x >= 2\n\nThus, minimum is 2. \nWith equality when x^(1/2) = 1 / [ x^(1/2)], or\n x = 1.\n\nDone.\n\nAlternative Method.\n\nOne can use two variable AM - GM,\nFor any two positive reals m and n, we have\n\n ( m + n )/ 2 >= (mn)^(1/2)\n\nWith equality if and only if m = n.\n\nJust set m = x and n = 1/x, to get,\n\n( x + 1/x )/ 2 >= 1\n\nor  x + 1/x >= 2\n\nAgain, the minimum values is 2 with equality if and only if x = 1 .\n\nRegards
1123620
<  Less Than\n> Greater Than
924405
Is it possible to have 2 equal signs in a problem?\nI am only in algebra but I haven't seen one like that before.\nSorry I couldn't help.
1138124
:equation when thing equally=0 \nEx:the proportion of negative=positive advantage & disadvantage copensated in its own value of property.anymore question??
967058
It depends on what you are wanting to prove. Generally speaking, when you substitute numbers, you are restricting to a specific example. You cannot prove a general result by only looking at specific examples (unless you somehow show those specific cases give *all* the possibilities). However, you *can* show a result is false, if it is false for some specific example, so to show a general result is false, it is enough to 'plug in numbers'.
461076
the value of the expression increases.\n\nUmm don't think so cuz negative numbers are real numbers and a negative number wouldnt make sense.
944997
you divide or multiply by a negative numberand the sign of inequality flips
900494
Equations are balanced- Hence the equal sign.  More information or a specific equation.