Which of the following is an example of an equation with no 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=3x+3
4 x plus 3 equals 3 x plus 3
3x+4=3x+3
3x+4=3x+4 is an example of an equation with no solution.
Which of the following is an example of an equation with exactly one solution?(1 point)
Responses
4x+3=4x+3
4 x plus 3 equals 4 x plus 3
3x+4=4x+3
3 x plus 4 equals 4 x plus 3
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
3x+4=3x+4
To determine which equation has no solution, we need to compare the coefficients and constants on both sides of the equation.
Let's examine each equation:
1) 3x+4=3x+4:
In this equation, the coefficients and constants on both sides of the equation are equal. Therefore, this equation has infinitely many solutions.
2) 3x+4=4x+3:
In this equation, the coefficients on the left side (3) and the right side (4) are different. Also, the constant on the left side (4) is different from the constant on the right side (3). Therefore, this equation has no solution.
3) 4x+3=3x+3:
In this equation, the coefficients on the left side (4) and the right side (3) are different. However, the constants on both sides of the equation are equal. Therefore, this equation also has no solution.
4) 3x+4=3x+3:
In this equation, the coefficients on the left side (3) and the right side (3) are equal. Also, the constants on both sides of the equation are different. Therefore, this equation has no solution.
So, the equation 3x+4=4x+3 is an example of an equation with no solution.
To determine which of the equations has no solution, we need to compare the coefficients and constants on both sides of the equation.
Let's analyze each equation step by step:
1. Equation: 3x + 4 = 3x + 4
Here, the coefficients (3) and the constants (4) are the same on both sides of the equation. Since the coefficients are the same, we can subtract 3x from both sides and subtract 4 from both sides:
3x - 3x + 4 - 4 = 3x - 3x + 4 - 4
0 = 0
After simplifying, we have 0 = 0. This equation is true for all values of x. Therefore, this equation has infinitely many solutions.
2. Equation: 3x + 4 = 4x + 3
Similarly, we compare the coefficients and constants on both sides. Here, the coefficients (3 and 4) are different, and the constants (4 and 3) are also different. To isolate x, subtract 3x from both sides and subtract 4 from both sides:
3x - 3x + 4 - 4 = 4x - 3x + 3 - 4
0 = x - 1
The equation x - 1 = 0 implies that x = 1. Therefore, there is one solution for this equation.
3. Equation: 4x + 3 = 3x + 3
Comparing the coefficients and constants on both sides, we can see that the coefficients (4 and 3) are different, but the constants (3 and 3) are the same. Subtracting 3x from both sides and subtracting 3 from both sides, we get:
4x - 3x + 3 - 3 = 3x - 3x + 3 - 3
x = 0
This equation has one solution, x = 0.
4. Equation: 3x + 4 = 3x + 3
When comparing the coefficients and constants in this equation, we notice that they are identical on both sides. This means that subtracting 3x from both sides and subtracting 4 from both sides won't change the equation:
3x - 3x + 4 - 4 = 3x - 3x + 3 - 4
0 = -1
After simplifying, we get 0 = -1. This equation is false for all values of x. Therefore, the equation 3x + 4 = 3x + 3 has no solution.
In conclusion, the equation 3x + 4 = 3x + 3 is an example of an equation with no solution.