Sure, let's go through the process of simplifying the expression step-by-step.
We start with the expression:
[tex]\[ 3x - 2x^2 + 10 - 7 - 5x^2 - x \][/tex]
First, let's collect all the like terms together. This involves grouping the [tex]\(x^2\)[/tex] terms, the [tex]\(x\)[/tex] terms, and the constant terms:
[tex]\[ -2x^2 - 5x^2 + 3x - x + 10 - 7 \][/tex]
Next, we combine the like terms:
1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[ -2x^2 - 5x^2 = -7x^2 \][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 3x - x = 2x \][/tex]
3. Combine the constant terms:
[tex]\[ 10 - 7 = 3 \][/tex]
Putting it all together, we have:
[tex]\[ -7x^2 + 2x + 3 \][/tex]
So, the simplified expression is:
[tex]\[ -7x^2 + 2x + 3 \][/tex]
