I have a problem that says:
Combine these two statements into a single mathematical statement:
x>2 and x<7.
I'm not sure if I'm supposed to do this by graphing a number line or not, is there a way to do it without a number line?
2 < x < 7
it is easy to visualize with a number line but I did not need one. By reading the statements you can figure out that x is between 2 and 7
If you have learned the interval notation, you could use:
(2,7) which means from 2 to 7, excluding 2 and 7. (inclusion would be [2,7]).
An equivalent notation that is in use would be:
]2,7[
When the square brackets are turned the right way, they also mean inclusion of the limits.
Yes, there is a way to combine the two statements without graphing a number line.
To combine the statements "x > 2" and "x < 7," you can use the logical operator "AND" (represented by the symbol "∧"). The combined statement will specify the range of values that satisfy both conditions simultaneously.
Here's how you can do it:
1. Start with the first statement: "x > 2." This means that x must be greater than 2.
2. Add the logical operator "AND" (∧).
3. Combine it with the second statement: "x < 7." This means that x must be less than 7.
Putting it all together, the combined statement is written as:
x > 2 ∧ x < 7
This expression indicates that x must satisfy both conditions—being greater than 2 and less than 7.
Remember, when combining statements, use the logical operators "AND" (represented by "∧") to express that both conditions must be true.