Which of the following equations has exactly one solution? (1 point)
0 -32 - 8 = 32 - 8
030-8=32+8
O -31+8 = -32 - 8
0 -8 + 3 = -8x + 3
0 -8 + 3 = -8x + 3
Solve for a to determine if the equation has one, none, or infinite solutions.
11x = 3 (7x - 1) - 10x (1 point)
O The equation has one solution: 2 = -1.
O The equation has no solution.
O The equation has one solution: 2 =
-3.
• The equation has infinite solutions.
To solve the equation 11x = 3(7x - 1) - 10x, we will simplify the equation and check for the number of solutions.
First, distribute the 3 on the right side of the equation:
11x = 21x - 3 - 10x
Combine like terms:
11x = 11x - 3
Subtract 11x from both sides:
0 = -3
This is a contradiction since we have 0 equal to a non-zero number (-3). Therefore, the equation has no solution.
The correct answer is: The equation has no solution.
Solve for a to determine if the equation has one, none, or infinite solutions.
5 (2x + 2) - 4 = 2x + 6 (1 point)
• The equation has one solution: ~ = 0.
O The equation has infinite solutions.
The equation has no solution.
O The equation has one solution: 2 = 1.
To solve the equation 5(2x + 2) - 4 = 2x + 6, we will simplify the equation and check for the number of solutions.
First, distribute the 5 on the left side of the equation:
10x + 10 - 4 = 2x + 6
Combine like terms:
10x + 6 = 2x + 6
Subtract 2x from both sides:
8x + 6 = 6
Subtract 6 from both sides:
8x = 0
Divide both sides by 8:
x = 0
The equation is linear and is solved for x. Therefore, the equation has one solution: x = 0.
The correct answer is: The equation has one solution: ~ = 0.
To determine which equation has exactly one solution, we need to solve each equation and count the number of solutions.
1. 0 - 32 - 8 = 32 - 8
Simplifying both sides of the equation, we get:
-40 = 24
Since -40 is not equal to 24, this equation has no solution.
2. 0 - 30 - 8 = 32 + 8
Simplifying both sides of the equation, we get:
-38 = 40
Again, -38 is not equal to 40, so this equation has no solution.
3. 0 - 31 + 8 = -32 - 8
Simplifying both sides of the equation, we get:
-23 = -40
Once more, -23 is not equal to -40, so this equation has no solution.
4. 0 - 8 + 3 = -8x + 3
Simplifying both sides of the equation, we get:
-5 = -8x
Dividing both sides by -8:
x = 5/8
Here, x = 5/8 is the unique solution to the equation.
Therefore, the equation "0 - 8 + 3 = -8x + 3" has exactly one solution.