Which of the following equations have exactly one solution?
2 answers:
For choice A, we can rearrange the equation to so it has exactly one solution,
For choice B, we rearrange the equation to so this too has exactly one solution,
Rearranging the equation in choice C by eliminating the terms gives us the false equality
so this equation has no solutions.
Eliminating in the equation in choice D gives the equality
which is always true, so this equation has infinitely many solutions.
Thus, we conclude that choices A and B work.
You might be interested in
Given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and by substituting their values into f(x) = 3x + 6. We will have the following:
<em><u>Given:</u></em>
- f(x) = 3x + 6
<em>We are told to find:</em>
- f(a)
- f(a + h), and
1. <em><u>Find f(a):</u></em>
- Substitute x = a into f(x) = 3x + 6
f(a) = 3(a) + 6
f(a) = 3a + 6
<em>2. Find f(a + h):</em>
- Substitute x = a + h into f(x) = 3x + 6
f(a + h) = 3(a + h) + 6
f(a + h) = 3a + 3h + 6
<em>3. Find </em><em>:</em>
- Plug in the values of f(a + h) and f(a) into
Thus:
- Add like terms
Therefore, given the function, <em>f(x) = 3x + 6,</em> we can solve for f(a), f(a + h) and by substituting their values into f(x) = 3x + 6. We will have the following:
Learn more here: