What is the solution to the quadratic inequality?

6x2≥10+11x

[−2/3,5/2]

[−3/2,1/4]

(−∞,−52]∪[23,∞)

(−∞,−23]∪[52,∞)

First, solve each inequality. I'll solve the first one first. 7 ≥ 2 x − 5 12 ≥ 2 x 6 ≥ x Therefore, x could be any number less than or equal to 6. In interval notation, this looks like: ( − ∞ , 6 ] The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  x be any number less than 6, but it could also be 6. Let's try the second example: 3 x − 2 4 > 4 3 x − 2 > 16 3 x > 18 x > 6 Therefore, x could be any number greater than 6, but x couldn't be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like: ( 6 , ∞ ) The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution). Now, the problem used the word "OR", meaning that either of these equations could be true. That means that either  x is on the interval  ( − ∞ , 6 ] or the interval  ( 6 , ∞ ) . In other words,  x is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  x could be any real number, since no matter what number  x is, it will fall in one of these intervals. The interval "all real numbers" is written like this: ( − ∞ , ∞ ) Final AnswerStep-by-step explanation:

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