Solve the equation.
3x+1=3(x−1)+4
(1 point)
Responses
x=1
x is equal to 1
No Solution
No Solution
Infinitely Many
Infinitely Many
x=1
To solve the equation 3x + 1 = 3(x - 1) + 4, we first need to simplify both sides of the equation.
Starting with the left side:
3x + 1
Now, let's simplify the right side.
3(x - 1) + 4
Distribute the 3:
3x - 3 + 4
Combine like terms:
3x + 1
Now that both sides are simplified, we can see that they are equal.
3x + 1 = 3x + 1
This means that this equation has infinitely many solutions.
To solve the given equation, we need to simplify and isolate the variable "x". Here are the steps:
1. Distribute 3 to the terms inside the parentheses on the right side of the equation:
3(x - 1) + 4 = 3x + 1
Expanding the equation gives us: 3x - 3 + 4 = 3x + 1
2. Combine like terms on both sides of the equation:
3x + 1 = 3x + 1
Notice that the variable "x" appears on both sides of the equation.
3. Subtract 3x from both sides of the equation to eliminate the variable on one side:
3x - 3x + 1 = 3x - 3x + 1
1 = 1
After simplifying, we see that the equation results in 1 = 1.
Now, we analyze the result:
- If both sides of the equation are equal (in this case, 1 = 1), it means that the equation is an identity. An identity implies that the equation is true for all values of "x".
Therefore, the answer to this equation is "Infinitely Many" solutions, as any value of "x" will satisfy the equation.