Question

simplify an expression for the model below. -x -x x -1 1 -1 1 1 -1 1 1

Explanation:

Step1: Count the x - terms

We have two \(-x\) terms and one \(x\) term. So the sum of the \(x\) - terms is \(-x - x+x\).
Simplifying the \(x\) - terms: \(-x - x+x=-x\) (because \(-x - x=-2x\) and \(-2x + x=-x\)).

Step2: Count the constant terms (the \(-1\) and \(1\) terms)

Count the number of \(-1\) terms: There are 3 \(-1\) terms, so the sum of \(-1\) terms is \(3\times(-1)= - 3\).
Count the number of \(1\) terms: Let's count the number of \(1\)s. In the second row, there are 2 \(1\)s, and in the third row, there are 2 \(1\)s, and in the first row, there is 1 \(1\). Wait, no, let's look at the figure again. The first row (top row) of the small squares: \(-1\), \(1\) (so 1 one). Second row: \(-1\), \(1\), \(1\) (so 2 ones). Third row: \(-1\), \(1\), \(1\) (so 2 ones). So total number of \(1\)s is \(1 + 2+2 = 5\). So the sum of the \(1\) terms is \(5\times1 = 5\).
Then the sum of the constant terms is \(-3 + 5=2\).

Step3: Combine the x - term and the constant term

Now, we combine the simplified \(x\) - term (\(-x\)) and the simplified constant term (\(2\)). So the simplified expression is \(-x + 2\) (or \(2 - x\)).

Answer:

\(-x + 2\) (or \(2 - x\))