Question

what is the solution set ( can any help me out)
x^2-x-11≥x-8

Answer 1

Everything outside of 3 and -1

Answer 2

x^2-x-11≥x-8

Since x contains the variable to solve for, move it to the left-hand side of the inequality by subtracting x from both sides.
x^2-x-11-x≥-8

According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both -x and -x.
x^2+(-1-1)x-11≥-8

Subtract 1 from -1 to get -2.
x^2+(-2)x-11≥-8

Remove the parentheses.
x^2-2x-11≥-8

Move 3 to the left-hand side of the equation by subtracting it from both sides. The goal is to have all terms on the left-hand side equal to 0.
x^2-2x-3≥0

In this problem 1*-3=-3 and 1-3=-2, so insert 1 as the right hand term of one factor and -3 as the right-hand term of the other factor.
(x+1)(x-3)≥0

Set each of the factors of the left-hand side of the inequality equal to 0 to find the critical points.
x+1=0_x-3=0

Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
x=-1_x-3=0

Set each of the factors of the left-hand side of the inequality equal to 0 to find the critical points.
x=-1_x-3=0

Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
x=-1_x=3

To find the solution set that makes the expression greater than 0, break the set into real number intervals based on the values found earlier.
x<=-1_-1<=x<=3_3<=x

Determine if the given interval makes each factor positive or negative. If the number of negative factors is odd, then the entire expression over this interval is negative. If the number of negative factors is even, then the entire expression over this interval is positive.
x<=-1 makes the expression positive_-1<=x<=3 makes the expression negative_3<=x makes the expression positive

Since this is a 'greater than 0' inequality, all intervals that make the expression positive are part of the solution.
x<=-1 or x≥3