Which equation has exactly ONE solution?
A. 3+10x/2 =4x + 2
B. 15x-5/3 = 5x + 4
C. 2+6x/2 =3x + 1
D. 4x-10/2 = 2x -5
To determine which equation has exactly one solution, we can solve each equation and see how many solutions there are.
A. 3+10x/2 =4x + 2
Multiplying both sides by 2 gives: 6 + 10x = 8x + 4
Subtracting 6x from both sides gives: 4x = -2
Dividing both sides by 4 gives: x = -2/4 = -1/2
B. 15x-5/3 = 5x + 4
Multiplying both sides by 3 gives: 45x - 5 = 15x + 12
Subtracting 15x from both sides gives: 30x - 5 = 12
Adding 5 to both sides gives: 30x = 17
Dividing both sides by 30 gives: x = 17/30
C. 2+6x/2 =3x + 1
Simplifying the left side gives: 2 + 3x = 3x + 1
Subtracting 3x from both sides gives: 2 = 1
This equation is not possible, as 2 does not equal 1.
D. 4x-10/2 = 2x -5
Simplifying the left side gives: 4x - 5 = 2x - 5
Subtracting 2x from both sides gives: 2x - 5 = -5
Adding 5 to both sides gives: 2x = 0
Dividing both sides by 2 gives: x = 0
From the solutions obtained, we can see that equation A and equation D both have exactly one solution.
Pick one of the answers given
Based on the solutions obtained, the equation D. 4x-10/2 = 2x -5 has exactly one solution.
To determine which equation has exactly one solution, we can use algebraic methods. The equation that has exactly one solution is the one where the variable is not eliminated and the equation simplifies to a unique value for the variable.
Let's solve each equation step-by-step:
A. 3+10x/2 = 4x + 2:
First, multiply both sides by 2 to eliminate the fraction:
2*(3+10x/2) = 2*(4x + 2)
6 + 10x = 8x + 4
Next, combine like terms:
10x - 8x = 4 - 6
2x = -2
Finally, divide both sides by 2:
x = -2/2
x = -1
B. 15x-5/3 = 5x + 4:
First, multiply both sides by 3 to eliminate the fraction:
3*(15x-5/3) = 3*(5x + 4)
15x - 5 = 15x + 12
Next, combine like terms:
15x - 15x = 12 + 5
0 = 17
We can see that 0 = 17 is not possible, so there is no solution for this equation.
C. 2+6x/2 = 3x + 1:
First, multiply both sides by 2 to eliminate the fraction:
2*(2+6x/2) = 2*(3x + 1)
4 + 6x = 6x + 2
Next, combine like terms:
6x - 6x = 2 - 4
0 = -2
We can see that 0 = -2 is not possible, so there is no solution for this equation.
D. 4x-10/2 = 2x - 5:
First, multiply both sides by 2 to eliminate the fraction:
2*(4x-10/2) = 2*(2x - 5)
8x - 10 = 4x - 10
Next, combine like terms:
8x - 4x = -10 + 10
4x = 0
Finally, divide both sides by 4:
x = 0/4
x = 0
Therefore, the equation that has exactly one solution is D. 4x-10/2 = 2x - 5, and the solution is x = 0.
To determine which equation has exactly one solution, we need to solve each equation and count the number of solutions.
Let's go through each equation:
A. 3 + 10x/2 = 4x + 2
To solve this equation, we can start by simplifying both sides:
3 + 5x = 4x + 2
Next, we can isolate the variable by subtracting 4x from both sides:
3 + x = 2
The variable x is alone on one side of the equation, so this equation has exactly one solution.
B. 15x - 5/3 = 5x + 4
To solve this equation, we can start by eliminating the fraction by multiplying both sides by 3:
45x - 5 = 15x + 12
Next, we can move all the x terms to one side and the constant terms to the other side:
45x - 15x = 12 + 5
30x = 17
To solve for x, we divide both sides by 30:
x = 17/30
Since x is a specific fraction, this equation does not have exactly one solution.
C. 2 + 6x/2 = 3x + 1
To solve this equation, we can start by simplifying both sides:
2 + 3x = 3x + 1
Next, we can isolate the variable x by subtracting 3x from both sides:
2 = 1
Uh-oh! We have a contradiction here. The equation simplifies to 2 = 1, which is not true. Therefore, this equation does not have any solution.
D. 4x - 10/2 = 2x - 5
To solve this equation, we can start by simplifying both sides:
4x - 5 = 2x - 5
Next, we can move all the x terms to one side and the constant terms to the other side:
4x - 2x = 5 - 5
2x = 0
To solve for x, we divide both sides by 2:
x = 0
Since x is a specific value, this equation has exactly one solution.
Therefore, the equation that has exactly one solution is option D: 4x - 10/2 = 2x - 5, with x = 0.