Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
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
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=3x+3
The equation "3x+4=3x+4" is an example of an equation with exactly one solution, as both sides of the equation are already equal, and there is no need to simplify or solve further.
@Bot are you right tho?
To determine which equation has exactly one solution, we need to compare the coefficients of x on both sides of the equation.
Let's analyze each option:
1. 3x + 4 = 3x + 4
The coefficients of x on both sides are the same, so this equation has infinitely many solutions.
2. 3x + 4 = 4x + 3
In this equation, the coefficients of x are different on both sides. It can be simplified as x = 1, so it has exactly one solution.
3. 4x + 3 = 4x + 3
The coefficients of x on both sides are the same, so this equation also has infinitely many solutions.
4. 3x + 4 = 3x + 3
Since the coefficients of x on both sides of the equation are the same, this equation can be simplified as 4 = 3, which is not true. Therefore, this equation has no solution.
Thus, the equation with exactly one solution is 3x + 4 = 4x + 3.
To determine which of the equations has exactly one solution, we need to analyze the equations and compare the coefficients and constants on both sides. Let's break down each equation and see if there is a unique solution:
1. 3x + 4 = 3x + 4
When we simplify this equation, we see that the variable terms (3x and 3x) and the constant terms (4 and 4) are exactly the same on both sides. This means that any value we substitute for 'x' will make the equation true. In other words, the equation is true for all values of 'x'. Therefore, this equation has infinitely many solutions.
2. 3x + 4 = 4x + 3
By comparing the coefficients and constants, we can see that the variable term on the left side (3x) is different from the variable term on the right side (4x). Since the coefficients are not the same, there cannot be a common solution for 'x'. Thus, this equation has one unique solution.
3. 4x + 3 = 4x + 3
Similar to the first equation, all the terms are the same on both sides. This means that any value we substitute for 'x' will make the equation true, giving us infinitely many solutions.
4. 3x + 4 = 3x + 3
By comparing the coefficients and constants, we can see that the constant term on the left side (4) is different from the constant term on the right side (3). Therefore, there cannot be a common solution for 'x'. This equation has no solution.
So, out of the given equations, only option 2, 3x + 4 = 4x + 3, has exactly one solution.