Simplification and Combining Terms

• Problem 1: Simplify $4x + 7x – 5x$

• Problem 3: Simplify $9y – 6 + 3y + 2$

• Problem 5: Simplify $2(p + 6) – 3p$

• Problem 6: Combine like terms: $8x + 5 – 3x – 2$

• Problem 7: Simplify $(x + 7) – (3x – 2)$

• Problem 9: Simplify $6(2y – 1) + y$

Evaluation Problems

• Problem 2: Evaluate $3a + 2b$ when $a = 5, b = 4$

• Problem 4: Find the value of $5m – 4$ when $m = 3$

• Problem 8: Evaluate the expression $4a – b$ when $a = 6, b = 2$

• Problem 10: Find the value of $10 – 2x$ when $x = 4$

Simplification and Combining Terms

• 1. $4x + 7x – 5x$

  • Explanation: Since all terms have the same variable ($x$), you simply perform the arithmetic on the coefficients: $4 + 7 = 11$, and $11 – 5 = 6$.

  • Result: $6x$

• 3. $9y – 6 + 3y + 2$

  • Explanation: Group the “like terms” together. Combine the $y$ terms ($9y + 3y = 12y$) and then combine the constants ($-6 + 2 = -4$).

  • Result: $12y – 4$

• 5. $2(p + 6) – 3p$

  • Explanation: First, use the Distributive Property to multiply $2$ by both terms inside the parentheses ($2 \cdot p + 2 \cdot 6 = 2p + 12$). Then, combine the result with the remaining term: $2p + 12 – 3p$. Finally, combine the $p$ terms ($2p – 3p = -p$).

  • Result: $-p + 12$

• 6. $8x + 5 – 3x – 2$

  • Explanation: Move the like terms next to each other: $(8x – 3x) + (5 – 2)$. Subtract the $x$ terms to get $5x$ and the constants to get $3$.

  • Result: $5x + 3$

• 7. $(x + 7) – (3x – 2)$

  • Explanation: The minus sign in front of the second parentheses applies to everything inside. Think of it as multiplying by $-1$. This changes the signs: $x + 7 – 3x + 2$. Now, combine like terms: $x – 3x = -2x$ and $7 + 2 = 9$.

  • Result: $-2x + 9$

• 9. $6(2y – 1) + y$

  • Explanation: Distribute the $6$ into the parentheses first ($6 \cdot 2y = 12y$ and $6 \cdot -1 = -6$). This gives you $12y – 6 + y$. Finally, add the $y$ terms together ($12y + y = 13y$).

  • Result: $13y – 6$

Evaluation Problems

• 2. $3a + 2b$ when $a = 5, b = 4$

  • Explanation: Substitute the numbers for the variables: $3(5) + 2(4)$. Multiply first ($15 + 8$), then add.

  • Result: $23$

• 4. $5m – 4$ when $m = 3$

  • Explanation: Replace $m$ with $3$: $5(3) – 4$. Multiply $5$ and $3$ to get $15$, then subtract $4$.

  • Result: $11$

• 8. $4a – b$ when $a = 6, b = 2$

  • Explanation: Plug in the values: $4(6) – 2$. Multiply $4$ by $6$ to get $24$, then subtract $2$.

  • Result: $22$

• 10. $10 – 2x$ when $x = 4$

  • Explanation: Substitute $4$ for $x$: $10 – 2(4)$. Follow the order of operations by multiplying $2 \cdot 4$ first ($10 – 8$), then subtract.

  • Result: $2$