How Many Solutions? Quick Check
4 of 54 of 5 Items
Question
Solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15(1 point)
Responses
The equation has no solution.
The equation has no solution.
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=0.
The equation has one solution: x equals 0 .
The equation has one solution: x=−10.
The equation has one solution: x equals negative 10 .
The equation has one solution: x=-10.
To determine if the equation 4x=3(x+5)-15 has one, none, or infinite solutions, we can simplify and solve for x:
4x = 3x + 15 - 15
4x = 3x
Subtracting 3x from both sides:
4x - 3x = 0
x = 0
Therefore, the equation has one solution: x = 0.
To determine how many solutions the equation has, we need to solve the equation and check the value of x.
The given equation is 4x = 3(x + 5) - 15.
To solve the equation, we will follow these steps:
Step 1: Distribute the 3 on the right side of the equation:
4x = 3x + 15 - 15
Simplifying, we have:
4x = 3x
Step 2: Subtract 3x from both sides to isolate x:
4x - 3x = 3x - 3x
Simplifying further, we have:
x = 0
So the value of x that satisfies the equation is x = 0.
Therefore, the equation has one solution: x = 0.