Which of the following is an example of an equation with no solution?(1 point)
Responses
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
3x+4=3x+3 is an example of an equation with no solution as the variable x gets eliminated from both sides of the equation resulting in an inconsistent statement, 4 = 3, which is not true.
Which of the following is an example of an equation with no solution?(1 point)
Responses
4x+3=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+4
3 x plus 4 equals 3 x plus 4
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
Ah, equations without solutions, the little troublemakers of algebra! Let's see which one fits the description.
4x+3=3x+3 - This equation can be solved. We just need to subtract 3x from each side of the equation. So, it's not the one.
3x+4=3x+4 - Well, this one is sort of a trick question. When you simplify it, you're left with 3=3, which means the equation is true, but there are infinite solutions! So, it's not the one either.
3x+4=4x+3 - Again, this one can be solved. Just subtract 3x from each side of the equation. So, not our winner.
Lastly, we have 3x+4=3x+3 - and bingo! This equation definitely has no solution. Even if we subtract 3x from each side, we're left with 4=3, which is simply not true.
So, the equation with no solution is 3x+4=3x+3. Keep your eyes peeled for these sneaky little equations!
To determine which equation has no solution, we need to analyze the coefficients and constants on both sides of the equation. In this case, the equation that has no solution is:
3x+4=3x+3
Since the coefficients of x on both sides are the same (3), we can subtract 3x from both sides of the equation to simplify it:
3x+4-3x=3x+3-3x
4 = 3
As you can see, the equation simplifies to 4 = 3, which is not a true statement. Therefore, the equation 3x+4=3x+3 has no solution.
To determine which of the given equations has no solution, we need to compare the coefficients and constants on both sides of the equation. If the coefficients and constants are equal on both sides, the equation will have infinitely many solutions. However, if the coefficients and constants are not equal on both sides, then the equation will have no solutions.
Let's analyze each equation:
1) 4x + 3 = 3x + 3
The coefficients on both sides are equal (4 and 3), but the constants (3 and 3) are equal as well. Therefore, this equation has infinitely many solutions.
2) 3x + 4 = 3x + 4
In this equation, both the coefficients and the constants are equal on both sides. Similar to the previous equation, this equation has infinitely many solutions.
3) 3x + 4 = 4x + 3
Here, the coefficients on both sides are not equal (3 and 4) and the constants (4 and 3) are also not equal. Therefore, this equation has no solution.
4) 3x + 4 = 3x + 3
In this equation, the coefficients on both sides are equal (3 and 3), but the constants (4 and 3) are not equal. Hence, this equation has no solution.
Thus, the equation with no solution is 3x + 4 = 3x + 3.