Answer:
What is a linear inequality ? A linear inequality has the same condition as a linear equality, but instead of the equal sign, we have for example this one ≤ wish means less than or equal to.
But what are the condition of a linear equality ? There are many ways of writing linear equations but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y") BUT the variables (x and y) on a linear equation do NOT have Exponents (like the 2 in x²) and square roots,
1. y < 3
Yes, this is a linear inequation. Frequently, the term linear equation refers implicitly to the case of just one variable (here y).
2. x ≥ 6
Yes.
3. x² > - 3
No, remember the rule the variable (here x) must not have exponents.
4. x - 3 > 1/2
Yes.
5. xy + 5 ≤ 7
This one is nice. If both x and y are variables then the answer is no, it's not a linear inequation. Why ?The linear equation is a sum of terms like "Ax" where x is a variable, and A is a number or a constant. On the other hand if x or y was a constant (like e or π), it could be treated as a number and the whole expression would become linear.
You can also have fun and write :
xy ≤ 2
for y > 0 we write:
x ≤ 2/y
x ≤ 2
and then simply say exponents are not allowed so not a linear inequation.