Which equation has exactly ONE solution?
Responses
A 8+3x2
= 13 + x8 + 3 x 2 = 13 + x
B 3+12x2
= 6x + 153 + 12 x 2 = 6x + 15
C 10+15x5
= 3x + 1010 + 15 x 5 = 3x + 10
D 4x−204
= x − 5
D 4x−204
= x − 5
incorrect its 8+3x2 = 13+x
The equation that has exactly one solution is D: 4x - 20 = x - 5.
To determine which equation has exactly one solution, we need to examine the equations and see if there is only one possible value for x that satisfies the equation.
Let's go through each equation:
A) 8 + 3x * 2 = 13 + x
To solve this equation, we need to simplify it first.
8 + 6x = 13 + x
Next, we can move the variables to one side and the constants to the other side.
6x - x = 13 - 8
5x = 5
To isolate x, we can divide both sides of the equation by 5.
x = 1
B) 3 + 12x * 2 = 6x + 15
Similar to the previous equation, we need to simplify it first.
3 + 24x = 6x + 15
Next, we can move the variables to one side and the constants to the other side.
24x - 6x = 15 - 3
18x = 12
To isolate x, we can divide both sides of the equation by 18.
x = 2/3
C) 10 + 15x * 5 = 3x + 10
Again, we need to simplify the equation.
10 + 75x = 3x + 10
Next, we can move the variables to one side and the constants to the other side.
75x - 3x = 10 - 10
72x = 0
Since any number multiplied by 0 is 0, all values of x satisfy this equation.
This means that there are infinite solutions.
D) 4x - 20 = x - 5
First, let's simplify the equation.
4x - x = 20 - 5
3x = 15
To isolate x, we can divide both sides of the equation by 3.
x = 5
Based on the analysis of the equations, the equation D) 4x - 20 = x - 5 has exactly one solution, which is x = 5.