Q: What is the set of all numbers that make the inequality true?

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x ≥ 6

Yes.

x ≥ -4

That is how an identity is defined. If the solution was not true for all numbers, then it would not be called an identity. In fact, it should be true for all complex numbers as well.

True.

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It means to find all the numbers for which the inequality is true.

Not unless you have an infinite amount of time as there are an infinite amount of numbers that are solutions to an inequality.

Since it is an inequality, there is no way to solve for x. It equals all real numbers.

x ≥ 6

that would be limited to 3 and -3 for values of x

Yes, it is true.

I assume you have inequalities that involve variables. If you replace the variable by some number, you will get an inequality that is either true or false. A value for the variable that results in a true statement is said to "satisfy" the inequality. For example, in: x + 3 > 10 If you replace x by 8, you get a true statement, since 11 is greater than 10; if you replace x by 7, you get a false statement, since 10 is not greater than 10. In this case, there are two inequalities; you have to find all numbers that satisfy both inequalities; in other words, that convert both inequalities into true statements.

First of all, if you have "Less than" or "Greater than" between your numbers, it means that you have an inequality, not an equation.The inequality is: 45

Take a sample point from either the top or bottom of the graph. I like to use (0,0) if it is not on the line. Substitute it into the inequality and if it is true then it represents all points on that line as true and vice versa.

Yes. Consider x2 â‰¥ 0

It is an inequality that defines all numbers (in the domain) such that they are not 3 or more.

It depends, many people do count 0 as a natural number, but MOST do not. So for most HS text book, the answer is NO, all whole numbers are not natural numbers and the reason is 0 is a whole number but not a natural number.