SOLUTION: Solve and graph the solution of the two inequalities |3x-7|is equal or greater than 23 (X-1)(x+3)(x2)<0

Question 971159: Solve and graph the solution of the two inequalities
|3x-7|is equal or greater than 23
(X-1)(x+3)(x2)<0
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
|3x-7| >= 23.

if the expression inside the absolute value sign is positive, then the absolute value of the expression is equal to the expression itself.

if the expression insides the absolute value sign is negative, then the absolute value of the expression is equal to the expression iteslf times - 1.

what this means is that you split the problem into two pieces.

you get 3x-7 >= 23 and you get -(3x-7) >= 23

when you take -(3x-7) >= 23 and multiply both sides of that equation by -1, you wind up with 3x-7 <= -23.

so you are dealing with 3x - 7 >= 23 and you are dealing with 3x-7 <= 23

solve 3x-7 >= 23 to get x >= 10.

solve 3x-7 <= -23 to get x <= -16/3

those are your solutions.

for (x-1)(x+3)(x^2) < 0, set it equal and solve for x.

you will get x = 1, x = -3, and x = 0.

those are the transition points in the grpah of that equation.

look at the intervals to the left of x = -3, between -3 and 0, between 0 and 1, and greater than 1.

see if the function is positive or negative in those intervals.

when x = -5, the function is positive.
when x = -1, the function is negative.
when x = .5, the function is negative.
when x = 5, the function is positive.

your solution should be that the function is negative between x = -3 and 0 and between x = 0 and x = 1

this can be written as:

-3 < x < 0 and 0 < x < 1

you can't include -3 or 0 or 1 because the function is < 0 and not <= 0.

here's a graph of the equation of y = (x-1)*(x+4)*(x^2)

RELATED QUESTIONS
Solve and graph the solution of |3x-7|greater or equal to 23... (answered by josgarithmetic)

Can I please have help with this, thank you! Graph the following systems of... (answered by Alan3354,ikleyn)

Solve and graph the solution: x+1 is greater than or equal to 7 and -6x is greater than... (answered by jsmallt9)

Solve and graph the solution set. A) 5y + 3 is less than or equal to -2 or -7 is... (answered by lwsshak3)

1.solve the system by addition. -2x+3y=-15 x-2y=11 I got -x+y=-4 that doesn't seem... (answered by jim_thompson5910)

Use the multiplication property of inequalities to solve the inequality. Graph the... (answered by lynnlo)

Solve and graph the following inequalities. If there is no solution, write DNE. If all... (answered by CubeyThePenguin)

Graph the system of inequalities. x+2y is less than or equal to 6 2x+y is less thab or... (answered by solver91311)

Graph the solution to the following inequalities on the number line. (x-2)(x+7)... (answered by stanbon)