solve for x to determine if the equation has one, none, or infinite solutions.
4x=3(x+5)−15(1 point)
The equation has one solution: x=−10.
The equation has no solution.
The equation has infinite solutions.
The equation has one solution: x=0.
To solve the equation, we will distribute 3 and -15:
4x = 3x + 15 - 15
Combining like terms:
4x = 3x
Now we subtract 3x on both sides:
4x - 3x = 3x - 3x
x = 0
Therefore, the equation has one solution: x = 0.
To determine the number of solutions for the equation 4x=3(x+5)−15, we need to simplify and solve for x.
Step 1: Distribute the 3 to the terms inside the parentheses:
4x = 3x + 15 - 15
Step 2: Combine like terms:
4x = 3x
Step 3: Subtract 3x from both sides:
4x - 3x = 0
x = 0
Since we have a single value for x, the equation has one solution: x=0.
To determine if the equation has one, none, or infinite solutions, we need to simplify and solve for x.
Let's start by distributing the 3 and -15 on the right side of the equation:
4x = 3x + 15 - 15
Simplifying further:
4x = 3x
Now, let's isolate x on one side by subtracting 3x from both sides:
4x - 3x = 3x - 3x
This simplifies to:
x = 0
So the equation has one solution: x = 0.
To verify this, we can substitute x=0 back into the original equation:
4(0) = 3(0 + 5) - 15
0 = 3(5) - 15
0 = 15 - 15
0 = 0
The equation holds true, which confirms that x = 0 is indeed the solution to the equation.
Therefore, the correct answer is: The equation has one solution: x = 0.