Complete the equation so that it has infinite solutions.(1 point)
4x+10= __ x+ __
fill in the blanks and check your work
4x+10=4x+10
In this case, the equation already has infinite solutions because both sides of the equation are identical.
Complete the equation so that it has no solution.(1 point)
5x+12= __ x+9.
Fill in the blank(s) and check your work
5x+12=5x+9-3
In this case, by subtracting 3 from both sides of the equation, we get:
5x+12=5x+9-3
The equation becomes:
5x+12=5x+6
Now, if we subtract 5x from both sides of the equation, we get:
12=6
Since 12 is not equal to 6, we find that there is no solution to this equation.
Complete the equation so that it has no solution.(1 point)
−7x−12= __ x+12
Fill in the blank(s) and check your work
−7x−12=−7x+12-24
In this case, by subtracting 24 from both sides of the equation, we get:
−7x−12=−7x+12-24
The equation becomes:
−7x−12=−7x-12
Now, if we subtract −7x from both sides of the equation, we get:
−12=−12
Since −12 is equal to −12, we find that every value of x will satisfy this equation. Therefore, it has infinite solutions.
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 no solution.
The equation has no solution.
The equation has one solution: x=−20.
The equation has one solution: x equals negative 20 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
To solve the equation 6(2x+4)-24=12x, we can start by simplifying the left side of the equation:
12x + 24 - 24 = 12x.
This simplifies to:
12x = 12x.
Now, if we subtract 12x from both sides of the equation, we get:
0 = 0.
Since 0 is equal to 0, we find that every value of x will satisfy this equation. Therefore, it has infinite solutions.
The equation has infinite solutions.
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
The equation "3x+4=4x+3" is an example of an equation with no solution. This is because both sides of the equation cannot be made equal by manipulating the variables.
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+4
3 x plus 4 equals 3 x plus 4
3x+4=3x+3