Identify each as True, False or Open. Answers may be used more than once or not at all.
Equation 1: 3(x − 4) + 2= 3x −1
True
To solve the equation, we will apply the distributive property by multiplying 3 to each term inside the parentheses:
3(x − 4) + 2 = 3x − 1
3x − 12 + 2 = 3x − 1
Now, combine like terms on both sides of the equation:
3x − 10 = 3x − 1
Since the variables cancel out on both sides, we can conclude that the equation is an open equation.
To identify whether the equation is true, false, or open, we need to solve the equation and check the equality. Let's simplify the equation step-by-step:
1. Distribute 3 to the terms inside the parentheses:
3(x - 4) + 2 = 3x - 1
3x - 12 + 2 = 3x - 1
2. Combine like terms on each side:
3x - 10 = 3x - 1
3. To solve for x, we want to isolate the variable on one side of the equation. However, in this case, both sides already have 3x terms. It seems like the equation is open because there is no solution that satisfies the equality.
Therefore, the answer for Equation 1 would be Open.