Question

how do u knwo which way to face the inequality sign in the answer of these questions like 1>x<3 how do u know which way to face them. i put some examples os u cna use them to explain

Answer 1

Using the graph identify the intervals:

a) Function being less than or equal to 0: In which x interval is the graph under the x-axis (the functions are less than 0 when they are under x-axis)

As the ineqaulity sing is less than or equal to 0, the interval includes those x-values for which the function is 0:

Solution: Interval from x=1 to x=3

`\begin{gathered} x^2-4x+3\leq0 \\ 1\leq x\leq3 \\ \lbrack1,3\rbrack \end{gathered}`

b) Function being greater than or equal to 0: In which x interval is the graph over the x-axis.

As the ineqaulity sing is greater than or equal to 0, the interval includes those x-values for which the function is 0:

Solution: Interval from - infinite to 1 and from 3 to infinite

`\begin{gathered} x^2-4x+3\ge0 \\ 1\ge x\ge3 \\ (-\infty,1\rbrack\cup\lbrack3,\infty) \end{gathered}`

c) Function being greater than 0: In which x interval is the graph over the x-axis.

As the ineqaulity sing is greater than to 0, the interval does not include those x-values for which the function is 0.

`\begin{gathered} x^2-4x+3>0 \\ 1>x>3 \\ (-\infty,1)\cup(3,\infty) \end{gathered}`

d) Function being less than 0: In which x interval is the graph under the x-axis.

As the ineqaulity sing is less than 0, the interval does not include those x-values for which the function is 0:

[tex]\begin{gathered} x^2-4x+3<0 \\ 1