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 \(y\) terms: There is only one \(y\) term, so it remains \(-4y\)
- Combine the constant terms: \(-4 + (-3) = -7\)
- Simplified expression: \(-4y - 7\)
Expression 5: \(-2k + (-4k) + 5\)
- Combine the \(k\) terms: \(-2k + (-4k) = -6k\)
- Combine the constant terms: There is only one constant term, so it 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 of \(-3z\): \(4z - (-3z) = 4z + 3z = 7z\)
- Simplified expression: \(7z\)
Expression 8: \(-2k - (-5) + 1\)
- Simplify the subtraction of \(-5\): \(-2k - (-5) = -2k + 5\)
- Combine the constant terms: \(5 + 1 = 6\)
- Simplified expression: \(-2k + 6\)
Expression 9: \(-4q - (-8q) + 10\)
- Simplify the subtraction of \(-8q\): \(-4q - (-8q) = -4q + 8q = 4q\)
- Combine the constant terms: There is only one constant term, so it 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 algebra worksheet 6th grade.
