Complete the equation so that it has no solution.(1 point)
5x+12=
x+9
To make the equation have no solution, we need to create a contradiction. One way to do this is to make the coefficients on the x terms unequal.
To achieve this, we can multiply the second equation by a non-zero constant. Let's choose -5:
5x + 12 = -5x - 45
Now we have:
5x + 12 = -5x - 45
Adding 5x to both sides:
10x + 12 = -45
Subtracting 12 from both sides:
10x = -57
Dividing by 10:
x = -57/10
So the solution is a single number, which means there is no solution that satisfies both equations simultaneously.
Complete the equation so that it has no solution.(1 point)
5x+12= x+9
Solve for x to determine if the equation has one, none, or infinite solutions.
6(2x+4)−24=12x
(1 point)
Responses
The equation has one solution: x=−20.
The equation has one solution: x equals negative 20 .
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
Which of the following is an example of an equation with no solution?(1 point)
Responses
3x+4=3x+3
3 x plus 4 equals 3 x plus 3
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
To complete the equation so that it has no solution, we need to set up an equation where the variable cancels out, resulting in a contradiction or an impossibility. In this case, we can use the distributive property to eliminate the variable.
Equation: 5x + 12 = (x + 9)
To eliminate the variable x, we can distribute the 5 on the left side of the equation:
5x + 12 = 5(x + 9)
Now, using the distributive property, we can simplify the right side:
5x + 12 = 5x + 45
Notice that both equations have the same term "5x" on the left side. By subtracting "5x" from both sides of the equation, we get:
12 = 45
However, this is a contradiction since 12 cannot equal 45. Hence, this equation has no solution.