5x + 12 = ___x +9
Complete the equation so that it has no solution
5x + 12 = 5x + 9
-7x - 12 = ___x + 12
Complete the equation so that it has no solution
-7x - 12 = -7x + 12
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 infinite solutions.
The equation has one solution: x=0
.
The equation has no solution.
The equation has one solution: x=−20
.
Let's solve the equation step by step:
6(2x+4) − 24 = 12x
Distributing the 6 on the left side of the equation:
12x + 24 - 24 = 12x
The 24 and -24 cancel out:
12x = 12x
The equation simplifies to:
0 = 0
Since both sides of the equation are equal, this means that the equation has infinite solutions.
pick an answer
The equation has infinite solutions.
Solve for x
to determine if the equation has one, none, or infinite solutions.
9(x+1)=3(5x+1)−12
The equation has no solution.
The equation has one solution: x=3
.
The equation has infinite solutions.
The equation has one solution: x=0
.
Let's solve the equation step by step:
9(x + 1) = 3(5x + 1) - 12
Expanding the parentheses on both sides:
9x + 9 = 15x + 3 - 12
Combining like terms:
9x + 9 = 15x - 9
Subtracting 9x from both sides:
9 = 6x - 9
Adding 9 to both sides:
18 = 6x
Dividing both sides by 6:
x = 3
So, the equation has one solution: x = 3.
Complete the equation so that it has infinite solutions
4x + 10 = ___x+ ___
To make the equation have infinite solutions, we can choose any value for the coefficients of x and the constants on the right side.
Let's complete the equation with coefficients of 1 for x and constants of -10 on the right side:
4x + 10 = x - 10
Which of the following is an example of an equation with no solution?
3x+4=4x+3
4x+3=3x+3
3x+4=3x+3
3x+4=3x+4
The equation "3x+4=4x+3" is an example of an equation with no solution.
Which of the following is an example of an equation with exactly one solution?
3x+4=4x+3
4x+3=4x+3
3x+4=3x+3
3x+4=3x+4
The equation "4x+3=4x+3" is an example of an equation with exactly one solution.
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x+2)−6=3x
The equation has one solution: x=3.
The equation has infinite solutions.
The equation has one solution: x=−3.
The equation has no solution.
Let's solve the equation step by step:
3(x + 2) - 6 = 3x
Expand the parentheses on the left side of the equation:
3x + 6 - 6 = 3x
The +6 and -6 on the left side of the equation cancel out:
3x = 3x
This equation indicates that the two sides are equal for any value of x. Therefore, the equation has infinite solutions.
pick an answer.
The equation has infinite solutions.
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15
The equation has no solution.
The equation has one solution: x=0.
The equation has one solution: x=−10.
The equation has infinite solutions.
Let's solve the equation step by step:
4x = 3(x+5) - 15
Distribute the 3 on the right side of the equation:
4x = 3x + 15 - 15
Simplify and combine like terms:
4x = 3x
Subtract 3x from both sides:
x = 0
So, the equation has one solution: x = 0.
Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6
The equation has no solution.
The equation has one solution: x=6.
The equation has infinite solutions.
The equation has one solution: x=10.
Let's solve the equation step by step:
5(2x+2) - 7x = 3x + 6
Distribute the 5 on the left side of the equation:
10x + 10 - 7x = 3x + 6
Combine like terms:
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
This implies that 10 is equal to 6, which is not true. Therefore, the equation has no solution.