In the expression \(-x - 7x + 6y + 8y\), we need to identify the like terms. Like terms are terms that have the same variable raised to the same power.
The terms \(-x\) and \(-7x\) are like terms because they both contain the variable \(x\).
The terms \(6y\) and \(8y\) are like terms because they both contain the variable \(y\).
Step 2: Combine Like Terms
Now, we combine the like terms by adding or subtracting their coefficients:
For the \(x\) terms: \(-x - 7x = -1x - 7x = -8x\)
For the \(y\) terms: \(6y + 8y = 14y\)
Final Answer
The simplified expression after combining like terms is: