To solve the problem of adding the given algebraic expressions, we need to combine like terms. Let's go through each part step by step.
a) \( x + 5 \) and \( x + 3 \)
\[
\begin{aligned}
&x + 5 \\
+ &x + 3 \\
\hline
&2x + 8
\end{aligned}
\]
- Combine the \( x \)-terms: \( x + x = 2x \)
- Combine the constant terms: \( 5 + 3 = 8 \)
Answer: \( 2x + 8 \)
---
b) \( 3x + 4 \) and \( 4x + 9 \)
\[
\begin{aligned}
&3x + 4 \\
+ &4x + 9 \\
\hline
&7x + 13
\end{aligned}
\]
- Combine the \( x \)-terms: \( 3x + 4x = 7x \)
- Combine the constant terms: \( 4 + 9 = 13 \)
Answer: \( 7x + 13 \)
---
c) \( 5y - 2 \) and \( 2y + 7 \)
\[
\begin{aligned}
&5y - 2 \\
+ &2y + 7 \\
\hline
&7y + 5
\end{aligned}
\]
- Combine the \( y \)-terms: \( 5y + 2y = 7y \)
- Combine the constant terms: \( -2 + 7 = 5 \)
Answer: \( 7y + 5 \)
---
d) \( 8y - 3 \) and \( 5y - 6 \)
\[
\begin{aligned}
&8y - 3 \\
+ &5y - 6 \\
\hline
&13y - 9
\end{aligned}
\]
- Combine the \( y \)-terms: \( 8y + 5y = 13y \)
- Combine the constant terms: \( -3 - 6 = -9 \)
Answer: \( 13y - 9 \)
---
e) \( 2a + 3b \) and \( 4a + 6b \)
\[
\begin{aligned}
&2a + 3b \\
+ &4a + 6b \\
\hline
&6a + 9b
\end{aligned}
\]
- Combine the \( a \)-terms: \( 2a + 4a = 6a \)
- Combine the \( b \)-terms: \( 3b + 6b = 9b \)
Answer: \( 6a + 9b \)
---
f) \( 5a - 2b \) and \( 7a - 3b \)
\[
\begin{aligned}
&5a - 2b \\
+ &7a - 3b \\
\hline
&12a - 5b
\end{aligned}
\]
- Combine the \( a \)-terms: \( 5a + 7a = 12a \)
- Combine the \( b \)-terms: \( -2b - 3b = -5b \)
Answer: \( 12a - 5b \)
---
Final Answers:
\[
\boxed{
\begin{aligned}
&\text{a) } 2x + 8 \\
&\text{b) } 7x + 13 \\
&\text{c) } 7y + 5 \\
&\text{d) } 13y - 9 \\
&\text{e) } 6a + 9b \\
&\text{f) } 12a - 5b
\end{aligned}
}
\]
Parent Tip: Review the logic above to help your child master the concept of addition of algebraic expressions worksheet.
