Which of the following is an example of an equation with exactly one solution?
1. 3x+4=3x+4
2. 4x+3=4x+3
3. 3x+4=3x+3
4. 3x+4=4x+3
AAAaannndd the bot gets it wrong yet again!
see the post after this one.
To find the equation with exactly one solution, we need to determine which equation has a unique solution, where the value of "x" is the same for both sides of the equation.
Let's analyze the given options:
1. 3x+4=3x+4:
Both sides of the equation are identical, so this equation has infinitely many solutions but not one unique solution.
2. 4x+3=4x+3:
Similar to the previous equation, both sides of the equation are identical, resulting in infinitely many solutions without a unique solution.
3. 3x+4=3x+3:
In this equation, the constant term (4 on the left side and 3 on the right side) is different. However, the terms involving "x" are the same on both sides, which means that if we subtract 3x from both sides, we are left with 4=3. This is not a true statement, so the equation has no solution.
4. 3x+4=4x+3:
This equation has different terms on both sides of the equation. To find the solution, we can proceed by simplifying the equation. Let's subtract 3x from both sides, which gives us x+4=3. Then, if we subtract 4 from both sides, we get x=-1. Thus, this equation has exactly one solution.
Therefore, the equation with exactly one solution is option 4: 3x+4=4x+3.
Which of the following is an example of an equation with exactly one solution
Option 1, "3x+4=3x+4," is a great example of an equation with exactly one solution. You see, both sides of the equation are identical, which means they perfectly coincide. Therefore, any value you plug in for "x" will make both sides equal and the equation true. It's like a hug between two clones - there can only be one perfect match!
The equation that has exactly one solution is the first one:
3x + 4 = 3x + 4
This equation has the same term on both sides of the equation, which means that if we subtract 3x from both sides, we are left with:
4 = 4
This is a true statement, which means that the equation is an identity and it is satisfied by any value of x. So, there is only one solution for this equation, that is, any real number.
On the other hand, the other equations have either no solutions or infinitely many solutions. For example, equation 3 has no solutions because 3x + 4 can never be equal to 3x + 3, no matter what value of x we choose. And equation 4 has infinitely many solutions because we can simplify it to x = 1/3 (or 3x - 3 = x, which gives us 2x = 3, or x = 3/2).