The problem presents a subtraction equation with a missing value: $x - (-3) = 8$. The goal is to find the value of $x$. The integer chip model shows that there are 11 positive chips, and 3 are crossed out, representing the subtraction of -3, leaving 8 positive chips.

1. Problem Description

The problem presents a subtraction equation with a missing value: $x - (-3) = 8$. The goal is to find the value of $x$. The integer chip model shows that there are 11 positive chips, and 3 are crossed out, representing the subtraction of -3, leaving 8 positive chips.

2. Solution Steps

We are given the equation:

$x - (-3) = 8$

We want to find the value of $x$. To do this, we can rewrite the subtraction of a negative number as addition:

$x + 3 = 8$

Now, we can subtract 3 from both sides of the equation to isolate $x$:

$x + 3 - 3 = 8 - 3$

$x = 5$

Based on the model, there are 8 positive chips remaining. Noah removed -3, so the original amount should have been $8 + (-3)$. The number of chips Noah started with is represented by the initial value $x$, and each positive chip is worth $+1$. Since subtracting -3 is the same as adding 3, the model indicates that the original number was

1

1. $x = 11$

$11 - (-3) = 11 + 3 = 14$ this doesn't equal 8 so this is wrong.

Instead, we have that $x - (-3) = 8$ which implies $x + 3 = 8$, subtracting 3 from both sides we have that $x = 5$.

The chip model shows 8 positive chips remaining after the 3 negative chips have been "removed". The model does not correspond with the equation if Noah only started with 5 chips and the problem describes positive chips only.

Noah started with an unknown number of positive chips.

He took away 3 negative chips.

After the removal, there are 8 positive chips left.

$x - (-3) = 8$. We are trying to find $x$.

Adding 3 to both sides of the equation, we get

$x - (-3) + (-3) = 8 + (-3)$

$x = 5$.

If $x = 5$ then the original expression is

$5 - (-3) = 5 + 3 = 8$, which is true.

3. Final Answer

5