Question

1. which expression is equivalent to $5x^2 + (-7x^2 + 3x) + 10 - (x + 1)$?

$-2x^2 + 2x + 9$ $12x^2 + 4x + 11$
$\circ$ a. $\circ$ b.
$-2x^2 + 2x + 11$ $2x^2 + 4x + 9$

Explanation:

Step1: Combine like terms for \(x^2\)

We have \(5x^2 + (-7x^2)\). Combining these, we get \(5x^2 - 7x^2 = -2x^2\).

Step2: Combine like terms for \(x\)

We have \(3x - x\) (after distributing the negative sign in \(-(x + 1)\) to get \(-x - 1\)). So \(3x - x = 2x\).

Step3: Combine constant terms

We have \(10 - 1 = 9\) (from \(10 - (x + 1)=10 - x - 1\)).

Step4: Combine all parts

Putting it all together, we have \(-2x^2 + 2x + 9\).

Answer:

\(-2x^2 + 2x + 9\) (corresponding to option a)