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 −10
True
To solve this equation, we will simplify and solve for x step-by-step.
Step 1: Distribute the 3 to both terms inside the parentheses.
3(x - 4) + 2 = 3x - 10
3 * x = 3x
3 * -4 = -12
So, the equation becomes:
3x - 12 + 2 = 3x - 10
Step 2: Combine like terms.
-12 + 2 = -10
-10 = -10
Now the equation becomes:
3x - 10 = 3x - 10
Step 3: Simplify further.
3x - 10 = 3x - 10
At this point, we can see that both sides of the equation are equivalent.
So, the answer is:
Open
To identify whether the equation is true, false, or open, we need to simplify both sides of the equation and then compare them.
Let's solve Equation 1 step by step:
1. Distribute the 3 to the terms inside the parentheses:
3(x - 4) + 2 = 3x - 10
3x - 12 + 2 = 3x - 10
2. Combine like terms on both sides:
3x - 10 = 3x - 10
3. Now, let's compare the simplified sides:
The left side of the equation is 3x - 10, and the right side after simplification is also 3x - 10.
Since both sides of the equation are equal, we can conclude that Equation 1 is an open equation.