Question

How do you write the interval [5,+infinity) as an inequality involving x and show each inequality using the real number line?

Answer 1

Hint: An algebraic inequality, such as x≥10, is read “x is greater than or equal to 10.” This inequality has infinitely many solutions for x. Some of the solutions are 22, 30, 30.5, 50, 20, and 20.001. Since it is impossible to list all of the solutions, a system is needed that allows a clear communication of this infinite set. Two common ways of expressing solutions to inequality are by graphing them on a number line and using interval notation.

Complete step by step answer:
In the above question, the interval is given and we have to find the inequality satisfying this.
We can see that the interval [5,+infinity) has two types of brackets, that is “[“ and “)”
The bracket “[“ means the number after it is included and “)” means the number is not included.
Hence the interval [5,+infinity) means 5 is included, thus it represents a number greater than and equal to 5.
We know that this type of inequality can be represented by x as,
\[x\ge 5\] or \[x-5\ge 0\]
Hence the inequality of the interval [5,+infinity) is given by \[x-5\ge 0\]
Now to represent an inequality on a real number line we draw a number line and darken the lines which satisfy the inequality, for representing infinity we draw an arrow at the end of the line representing the x at the positive or negative side depending upon +infinity or -infinity.

Note:
While representing intervals of inequality we do not include infinity, that is we do not use “]” after or before infinity. In number line representation the point included is represented by a solid dot and the point which is not included is represented by a void or hollow dot.