Let's start by breaking down the expression step-by-step and simplifying it. We have:
[tex]\[7 \left[(4x - 6) - (8 - 2x) - (-12x + 24) + 40 - 14\right]\][/tex]
First, let's handle the operations inside the brackets [tex]\((...)\)[/tex].
1. Expand and simplify the terms inside the brackets:
[tex]\[
(4x - 6) - (8 - 2x) - (-12x + 24) + 40 - 14
\][/tex]
2. Distribute the negatives:
[tex]\[
4x - 6 - 8 + 2x + 12x - 24 + 40 - 14
\][/tex]
3. Combine like terms (all [tex]\(x\)[/tex] terms first, and all constant terms together):
- [tex]\(x\)[/tex] terms: [tex]\(4x + 2x + 12x = 18x\)[/tex]
- Constant terms: [tex]\(-6 - 8 - 24 + 40 - 14 = -12\)[/tex]
4. So, the expression inside the brackets simplifies to:
[tex]\[
18x - 12
\][/tex]
Next, we need to multiply this simplified expression by 7:
[tex]\[
7 \times (18x - 12)
\][/tex]
Distribute the 7:
[tex]\[
7 \times 18x - 7 \times 12 = 126x - 84
\][/tex]
Therefore, the simplified result of the given expression is:
[tex]\[
126x - 84
\][/tex]
