How can you solve this quadratic inequality by using the interval method?2(xsquared) - 9 > 23 thanks

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embizze | High School Teacher | (Level 2) Educator Emeritus

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Solve `2x^2-9>23` .

(1) First we rewrite as an equivalent inequality. (An equivalent inequality has the same solution set)


(2) Factor the left-hand side as `2(x^2-16)>0` or `2(x+4)(x-4)>0` .

(3) Note that the zeros occur at x=-4 and x=4. Then we divide the x-axis into 3 intervals: `(-oo,-4),(-4,4),(4,oo)` .

(4) Choose a point in each interval and compute the value of the function.


(5) Then the solution set is `(-oo,-4)uu(4,oo)` or `x<-4,x>4`

As a check, the graph:

` <img style="width: 300px; height: 200px; vertical-align: middle; float: none;" _mce_style="width: 300px; height: 200px; vertical-align: middle; float: none;" src="" _mce_src="" sscr="-7.5,7.5,-5,30,1,1,1,1,1,300,200,func,2x^2-9,null,0,0,,,black,1,none,func,23,null,0,0,,,black,1,none" script=" "> `

Note that the graph is above the line y=23 to the left of -4, and to the right of 4 as found above.

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