Final Answer:
It seems like there might be a formatting issue in the question, specifically with the symbol ">" and the values "1" and "3."
Typically, inequalities are written in the form
- The solution for a) is all real numbers less than 1.
- The solution for b) is all real numbers greater than 1.
- The solution for c) is all real numbers greater than 3.
- The solution for d) is all real numbers less than 3.
Step-by-step explanation:
It seems like there might be some confusion in the way the inequality is presented, with the extra quotation marks suggesting a possible typo. However, assuming we are dealing with simple linear inequalities without the quote marks, I will provide an explanation for each:
a) \( x < 1 \)
This inequality indicates that x can be any real number less than 1. This does not include 1 itself, so x can be 0.9, -5, -3.14159, etc. Graphically, this is represented on a number line with an open circle at 1 and a shaded line extending to the left, indicating all values less than 1.
b) \( x > 1 \)
This inequality indicates that x can be any real number greater than 1. This also does not include 1 itself, so x can be 1.1, 2, 10, 100, etc. On a number line, it would be represented with an open circle at 1, and the shading going to the right, which represents all numbers greater than 1.
c) \( x > 3 \)
This is similar to the previous inequality, but instead of 1, the reference point is 3. Therefore, x can be any real number greater than 3. It does not include 3, so x could be 3.1, 4, or 8.2, for instance. On a number line, an open circle would be placed at 3, and the line shaded to the right to show all the numbers greater than 3.
d) \( x < 3 \)
This inequality states that x can be any real number less than 3. Again, 3 is not included, so x could be 2.999, 0, or -7, among other values. On the number line, this would be represented by an open circle at 3, with the line shaded to the left, representing all numbers less than 3.
In conclusion:
- The solution for a) is all real numbers less than 1.
- The solution for b) is all real numbers greater than 1.
- The solution for c) is all real numbers greater than 3.
- The solution for d) is all real numbers less than 3.