Certainly! Let's simplify the given mathematical expression step-by-step:
Given expression:
[tex]\[ 2x + 9x + (-4b + 8b + (-2x + 9x)) \][/tex]
1. Simplify the innermost expression:
[tex]\[ -2x + 9x \][/tex]
Combine like terms:
[tex]\[ (-2 + 9)x = 7x \][/tex]
Now the expression becomes:
[tex]\[ 2x + 9x + (-4b + 8b + 7x) \][/tex]
2. Simplify within the parentheses involving [tex]\( b \)[/tex]:
[tex]\[ -4b + 8b \][/tex]
Combine like terms:
[tex]\[ (-4 + 8)b = 4b \][/tex]
Now the expression becomes:
[tex]\[ 2x + 9x + (4b + 7x) \][/tex]
3. Expand and combine all [tex]\( x \)[/tex] terms:
[tex]\[ 2x + 9x + 7x \][/tex]
Combine like terms:
[tex]\[ (2 + 9 + 7)x = 18x \][/tex]
Now we have:
[tex]\[ 18x + 4b \][/tex]
4. Final simplified expression:
[tex]\[ 4b + 18x \][/tex]
This is the simplified form of the given expression.
