 # 4 - Sign charts

Sign charts are usefull to solve inequalities. Read carefully the following examples, it will help you understand :

*** How to solve .

If both factors in a product are positive (or negative), then the product is positive too. Hence the sign of (2 x - 2)(4 x + 16) depends on the sign of its two factors.
Let's find the signs of the two factors thanks to 2 equations :  The first factor is positive whenever , so you write down + on the right of the number 1; the second is positive when , so you write down + on the right of the number -4. To determine the sign of a product, you draw a table : on every line, there will be the sign of a factor. On the last line, you multiply the two lines above. On the last line, we can see that whenever .
-4 and 1 are excluded from the set of solutions because the inequality can't be an equality.

*** How to solve It is the same thing, the sign of a quotient depends on the sign of the numerator and the sign of the denominator. There is just a difference : you can't divide by zero. So you draw a double bar in the table, under the "forbidden" value.   is positive whenever , and whenever . 5 is excluded from the set of solutions. When there is a double bar, the value below is always excluded from the set of solutions. In that case, we are looking for negative or null values ; finally, the solutions are : .

*** How to solve      >>> Trigonometry lesson >>>

Signs charts

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