Question

An equation that has
choose your answer...
is never true, no matter what the value of x is.
An equation that has
choose your answer...
is always true, no matter what the value of x is.

Answer 1

In mathematical terms, the statements you're looking for can be expressed as follows:

1. An equation that has **no solution** is never true, no matter what the value of x is.
2. An equation that has **all real numbers as solutions** is always true, no matter what the value of x is.

For example:
- An equation like \(x + 1 = x + 2\) has no solution because there's no value of x that can satisfy it.
- An equation like \(2(x + 1) = 2x + 2\) is always true for any value of x because both sides are equivalent.

Answer 2

Answers are
One solution
Infinite solutions
No solutions

Answer 3

Thank you for providing the options. Here’s how they fit into your original statements:

1. An equation that has **no solutions** is never true, no matter what the value of \(x\) is.

2. An equation that has **infinite solutions** is always true, no matter what the value of \(x\) is.

So, you can fill in your statements as follows:

- An equation that has **no solutions** is never true, no matter what the value of \(x\) is.
- An equation that has **infinite solutions** is always true, no matter what the value of \(x\) is.