Sure, let's simplify the given expression step-by-step:
[tex]\[ [(4x - 6) - (8 - 2x) - (-12x + 24) + 40 - 14] \][/tex]
1. Distribute the negative signs inside the parentheses:
- For the second term:
[tex]\[ -(8 - 2x) \][/tex]
This becomes:
[tex]\[ -8 + 2x \][/tex]
- For the third term:
[tex]\[ -(-12x + 24) \][/tex]
This becomes:
[tex]\[ +12x - 24 \][/tex]
Substituting these into the original expression, we get:
[tex]\[ (4x - 6) - 8 + 2x + 12x - 24 + 40 - 14 \][/tex]
2. Combine the like terms:
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ 4x + 2x + 12x \][/tex]
This results in:
[tex]\[ 18x \][/tex]
- Combine the constant terms:
[tex]\[ -6 - 8 - 24 + 40 - 14 = -12 \][/tex]
Therefore, the simplified expression is:
[tex]\[ 18x - 12 \][/tex]
The expression simplifies to:
[tex]\[ \boxed{18x - 12} \][/tex]
In summary, by distributing the negative signs and combining like terms, we simplify the original expression to [tex]\(18x - 12\)[/tex].
