Problem 1: Simplify $3x + 5x – 2x$.
Problem 3: Simplify $7y – 3 + 2y + 5$.
Problem 5: Simplify $5(p – 2) + 3p$.
Problem 6: Combine like terms: $6m + 4n – 2m + n$.
Problem 7: Simplify $(x + 4) – (2x – 3)$.
Problem 2: Evaluate the expression $2a + 3b$ when $a = 4$ and $b = 5$.
Problem 4: Find the value of $4x – 3$ when $x = 6$.
Problem 8: Evaluate $15 + 6 \div 3 \times 4$.
Problem 9: Simplify using BODMAS: $(18 – 6) \div 3 + 5$.
Problem 10: Find the value of $20 – 4^2 + 6$.
1. $3x + 5x – 2x = 6x$ Explanation: Since all terms have the same variable ($x$), you simply combine the coefficients: $3 + 5 = 8$, and $8 – 2 = 6$.
3. $7y – 3 + 2y + 5 = 9y + 2$ Explanation: Group “like terms” together. Add the variable terms ($7y + 2y = 9y$) and the constant numbers ($-3 + 5 = 2$).
5. $5(p – 2) + 3p = 8p – 10$ Explanation: First, distribute the $5$ into the parentheses ($5 \times p$ and $5 \times -2$) to get $5p – 10$. Then, add the remaining $3p$: $5p + 3p – 10 = 8p – 10$.
6. $6m + 4n – 2m + n = 4m + 5n$ Explanation: You can only combine terms with the same letters. Subtract the $m$ terms ($6m – 2m = 4m$) and add the $n$ terms ($4n + 1n = 5n$).
7. $(x + 4) – (2x – 3) = -x + 7$ Explanation: The minus sign in front of the second parenthesis changes the signs inside: $x + 4 – 2x + 3$. Then combine like terms: $x – 2x = -x$ and $4 + 3 = 7$.
2. Evaluate $2a + 3b$ when $a = 4, b = 5$: Result is $23$ Explanation: Replace $a$ with $4$ and $b$ with $5$. Calculate $(2 \times 4) + (3 \times 5)$, which is $8 + 15 = 23$.
4. Value of $4x – 3$ when $x = 6$: Result is $21$ Explanation: Substitute $6$ for $x$. Multiply first ($4 \times 6 = 24$), then subtract $3$ to get $21$.
8. $15 + 6 \div 3 \times 4 = 23$ Explanation: Following BODMAS, perform Division first ($6 \div 3 = 2$), then Multiplication ($2 \times 4 = 8$), and finally Addition ($15 + 8 = 23$).
9. $(18 – 6) \div 3 + 5 = 9$ Explanation: Start with the Brackets ($18 – 6 = 12$). Then Divide ($12 \div 3 = 4$), and finally Add ($4 + 5 = 9$).
10. $20 – 4^2 + 6 = 10$ Explanation: Handle the Order/Power first ($4^2 = 16$). The expression becomes $20 – 16 + 6$. Moving left to right, $20 – 16 = 4$, and $4 + 6 = 10$.