Which of the following is an example of an equation with no solution?
A. 4x + 3 = 3x + 3
B. 3x + 4 = 4x + 3
C. 3x + 4 = 3x + 3
D. 3x + 4 = 3x + 4
C. 3x + 4 = 3x + 3
Which of the following is an example of an equation with exactly one solution?
A. 4x + 3 = 4x + 3
B. 3x + 4 = 4x + 3
C. 3x + 4 = 3x + 3
D. 3x + 4 = 3x + 4
D. 3x + 4 = 3x + 4
Solve for x to determine if the equation has one, none, or infinite solutions.
3(x + 2) - 6 = 3x
A. the equation has no solution
B. the equation has infinite solutions
C. the equation has one solution: x = 3
D. the equation has one solution: x = -3
To solve the equation 3(x + 2) - 6 = 3x, we can start by distributing the 3 on the left side:
3x + 6 - 6 = 3x
We can simplify the equation:
3x = 3x
The variables are the same on both sides of the equation, and the equation is simplified to 3x = 3x. This means that the equation has infinite solutions.
Therefore, the answer is:
B. the equation has infinite solutions
Solve for x to determine if the equation has one, none, or infinite solutions
4x = 3(x + 5) - 15
A. the equation has no solution
B. the equation has infinite solutions
C. the equation has one solution : x = 0
D. the equation has one solution: x = -10
To solve the equation 4x = 3(x + 5) - 15, we can start by distributing the 3 on the right side:
4x = 3x + 15 - 15
Simplifying further:
4x = 3x
The variables are the same on both sides of the equation, and the equation is simplified to 4x = 3x. This means that the equation has infinite solutions.
Therefore, the answer is:
B. the equation has infinite solutions
Solve for x to determine if the equation has one, none, or infinite solutions
5(2x + 2) - 7x = 3x + 6
A. the equation has one solution: x = 10
B. the equation has no solution
C. the equation has infinite solutions
D. the equation has one solution: x = 6
To solve the equation 5(2x + 2) - 7x = 3x + 6, we can start by simplifying the equation:
10x + 10 - 7x = 3x + 6
Combine like terms:
3x + 10 = 3x + 6
Subtract 3x from both sides to eliminate the variables on one side:
10 = 6
The equation 10 = 6 is not true, which means there is no solution to the equation.
Therefore, the answer is:
B. the equation has no solution