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[Music] in this video we're going to look at change of sign and change design is a very useful technique to find where solution to an equation might lie particularly if the equation is very difficult won't solve so here we've got an example now this example is actually an equation which is very simple to solve uh we can probably solve in our height straight away and get the answer 3.5 but what i've done is i've said the first example it showed the equation 2x minus 7 equals 0 has a solution between x equals three and x equals four and what i've done also is i've drawn the graph y equals two x minus seven now the reason i've drawn that is if the equation equals zero if you draw the graph y equals and what the equation is on the other side not the zero point of the other part you're going to get y equals 2x minus 7. if we draw that graph you'll find that that graph crosses the x-axis of 3.5 which was the solution to the equation and the reason it's the solution is well if we've got the...