math
9th Grade - Sign charts

9th Grade lesson

4 - Sign charts


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


*** How to solve equation.

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 :
equation
equation
The first factor is positive whenever equation, so you write down + on the right of the number 1; the second is positive when equation, 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.

tableau de signe avec produit

On the last line, we can see that equation whenever equation solutions.
-4 and 1 are excluded from the set of solutions because the inequality can't be an equality.



*** How to solve solve with Sign chart

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.
equation
equation
math is positive whenever equation, and equation whenever equation.

Sign chart avec quotient

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 : equation solution with quotient.



*** How to solve equation solution
equation solution
equation solution
equation solution
Sign chart

equation solution resolue avec un Sign chart




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