Leonardo wrote an equation that has an infinite number of solutions. One of the terms in Leonardo’s equation is missing, as shown below.

Question

Negative (x minus 1) + 5 = 2 (x + 3) minus box

Which could be the missing term that Leonardo put into the box?
x
3x
1
5

Answer 1

Let's start by simplifying the provided equation step by step. The equation given is:

\[ -(x - 1) + 5 = 2(x + 3) - \text{box} \]

First, simplify the left side:

1. Distribute the negative sign: \[ -x + 1 + 5 = -x + 6 \]

So, the left side becomes:

\[ -x + 6 \]

Now simplifying the right side:

1. Distribute the 2: \[ 2(x + 3) = 2x + 6 \]
2. So the right side becomes: \[ 2x + 6 - \text{box} \]

Now we can rewrite the entire equation as:

\[ -x + 6 = 2x + 6 - \text{box} \]

Next, to simplify the equation further, we can isolate the terms involving \(\text{box}\):

1. Move all \(x\) terms to one side and constant terms to the other side: \[ -x - 2x + 6 = 6 - \text{box} \] This simplifies to: \[ -3x + 6 = 6 - \text{box} \]

Now, subtract \(6\) from both sides:

\[ -3x = - \text{box} \]

Rearranging gives:

\[ \text{box} = 3x \]

Since the question asks for possible options for the box that will have an infinite number of solutions, the term must be \(3x\) as it allows the left and right sides to retain equivalency for all values of \(x\):

Thus, the missing term that Leonardo put into the box must be:

\[ \text{box} = 3x \]

So, the correct option is \(3x\).