To solve the problem, we need to combine like terms in each expression. Like terms are terms that have the same variable raised to the same power. We will simplify each expression step by step.
Expression 1: \(2r + 1 + (-4r) + 7\)
- Combine the \(r\) terms: \(2r + (-4r) = -2r\)
- Combine the constant terms: \(1 + 7 = 8\)
- Simplified expression: \(-2r + 8\)
Expression 2: \(3z + 2 + (-5z) + 6\)
- Combine the \(z\) terms: \(3z + (-5z) = -2z\)
- Combine the constant terms: \(2 + 6 = 8\)
- Simplified expression: \(-2z + 8\)
Expression 3: \(-3z - z\)
- Combine the \(z\) terms: \(-3z - z = -4z\)
- Simplified expression: \(-4z\)
Expression 4: \(-4y - 4 + (-3)\)
- Combine the constant terms: \(-4 + (-3) = -7\)
- Simplified expression: \(-4y - 7\)
Expression 5: \(-2k + (-4k) + 5\)
- Combine the \(k\) terms: \(-2k + (-4k) = -6k\)
- The constant term remains: \(5\)
- Simplified expression: \(-6k + 5\)
Expression 6: \(4t + 2 + (-3t) + 6\)
- Combine the \(t\) terms: \(4t + (-3t) = t\)
- Combine the constant terms: \(2 + 6 = 8\)
- Simplified expression: \(t + 8\)
Expression 7: \(4z - (-3z)\)
- Simplify the subtraction: \(4z - (-3z) = 4z + 3z = 7z\)
- Simplified expression: \(7z\)
Expression 8: \(-2k - (-5) + 1\)
- Simplify the subtraction: \(-2k - (-5) = -2k + 5\)
- Combine the constant terms: \(5 + 1 = 6\)
- Simplified expression: \(-2k + 6\)
Expression 9: \(-4q - (-8q) + 10\)
- Simplify the subtraction: \(-4q - (-8q) = -4q + 8q = 4q\)
- The constant term remains: \(10\)
- Simplified expression: \(4q + 10\)
Expression 10: \(-4h + 3 + (-2h) + 3\)
- Combine the \(h\) terms: \(-4h + (-2h) = -6h\)
- Combine the constant terms: \(3 + 3 = 6\)
- Simplified expression: \(-6h + 6\)
Final Answer:
\[
\boxed{
\begin{array}{|c|c|}
\hline
2r + 1 + (-4r) + 7 & -2r + 8 \\
3z + 2 + (-5z) + 6 & -2z + 8 \\
-3z - z & -4z \\
-4y - 4 + (-3) & -4y - 7 \\
-2k + (-4k) + 5 & -6k + 5 \\
4t + 2 + (-3t) + 6 & t + 8 \\
4z - (-3z) & 7z \\
-2k - (-5) + 1 & -2k + 6 \\
-4q - (-8q) + 10 & 4q + 10 \\
-4h + 3 + (-2h) + 3 & -6h + 6 \\
\hline
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of algebraic expression 6th grade worksheet.
