Sure, let's simplify the given expression step-by-step.
The original expression is:
[tex]\[ 5y - \frac{7}{2} + 5x - z - 8x + y \][/tex]
1. Combine like terms involving [tex]\( y \)[/tex]:
- [tex]\( 5y \)[/tex] and [tex]\( y \)[/tex] are like terms.
- Adding them together: [tex]\( 5y + y = 6y \)[/tex].
2. Combine like terms involving [tex]\( x \)[/tex]:
- [tex]\( 5x \)[/tex] and [tex]\( -8x \)[/tex] are like terms.
- Adding them together: [tex]\( 5x - 8x = -3x \)[/tex].
3. Combine all the terms:
- Now substitute the simplified terms back into the expression.
- We get: [tex]\( 6y - 3x - z - \frac{7}{2} \)[/tex].
Therefore, the simplified expression is:
[tex]\[ -3x + 6y - z - \frac{7}{2} \][/tex]
