Answer key for a distributive property and combining like terms puzzle activity.

Let’s solve each expression step by step using the distributive property and then combine like terms.

---

1.

Expression:
x + 20 + 2(x – 5) + 5x

Step 1: Distribute the 2 into (x – 5):
→ 2 * x = 2x
→ 2 * (-5) = -10
So now:
x + 20 + 2x – 10 + 5x

Step 2: Combine like terms:
x + 2x + 5x = 8x
20 – 10 = 10
→ Final: 8x + 10

---

2.

Expression:
4(x + 8) + 6(x – 4)

Step 1: Distribute:
4*x = 4x, 4*8 = 32 → 4x + 32
6*x = 6x, 6*(-4) = -24 → 6x – 24

Now combine:
4x + 32 + 6x – 24

Step 2: Combine like terms:
4x + 6x = 10x
32 – 24 = 8
→ Final: 10x + 8

Wait — let me check again. The answer key says “8 + 10x” — that’s the same as 10x + 8. So yes, correct.

But looking at the image, it shows “8 + 10x” for this one — so we’ll write it as 8 + 10x to match.

Actually, order doesn’t matter in addition, but since the key writes constants first sometimes, we can follow that style if needed. But mathematically, both are fine.

We’ll keep it as 10x + 8, unless specified otherwise. But let’s double-check the problem layout.

Looking back — actually, in the hexagon grid, the top middle is labeled “8 + 10x”, which matches our result. So we’re good.

---

3.

Expression:
9 + 8(4 – 6x) – 2x

Step 1: Distribute 8 into (4 – 6x):
8*4 = 32
8*(-6x) = -48x
So:
9 + 32 – 48x – 2x

Step 2: Combine like terms:
Constants: 9 + 32 = 41
Variables: -48x – 2x = -50x
→ Final: 41 – 50x or -50x + 41

The key shows “41 – 50x” — perfect.

---

4.

Expression:
7(x + 2) – 8 + x

Step 1: Distribute 7:
7*x = 7x, 7*2 = 14 → 7x + 14
Then: 7x + 14 – 8 + x

Step 2: Combine like terms:
7x + x = 8x
14 – 8 = 6
→ Final: 8x + 6

Key shows “8x + 6” — correct.

---

5.

Expression:
4x + 2(x + 16) – 14

Step 1: Distribute 2:
2*x = 2x, 2*16 = 32 → 4x + 2x + 32 – 14

Step 2: Combine:
4x + 2x = 6x
32 – 14 = 18
→ Final: 6x + 18

Key shows “6x + 18” — correct.

---

6.

Expression:
11x + 5

This is already simplified! No parentheses, no like terms to combine.
→ Final: 11x + 5

Matches key.

---

7.

Expression:
–(9 + 2x) + 8 + 7x

Step 1: Distribute the negative sign (which is like multiplying by -1):
-1*(9) = -9
-1*(2x) = -2x
So: -9 – 2x + 8 + 7x

Step 2: Combine like terms:
Constants: -9 + 8 = -1
Variables: -2x + 7x = 5x
→ Final: 5x – 1

Key shows “5x – 1” — correct.

---

8.

Expression:
(x + 5) + 3(x + 2)

Step 1: Distribute 3:
3*x = 3x, 3*2 = 6 → x + 5 + 3x + 6

Step 2: Combine:
x + 3x = 4x
5 + 6 = 11
→ Final: 4x + 11

Key shows “4x + 11” — correct.

---

9.

Expression:
4x + 2

Already simplified.
→ Final: 4x + 2

Matches key.

---

10.

Expression:
5 + 2 + 29 + (9 + x)5

First, simplify inside: (9 + x)5 means 5*(9 + x)

Step 1: Rewrite:
5 + 2 + 29 + 5*(9 + x)

Step 2: Add constants outside: 5 + 2 + 29 = 36
Distribute 5: 5*9 = 45, 5*x = 5x → 45 + 5x

Now total: 36 + 45 + 5x = 81 + 5x
→ Final: 5x + 81

Key shows “5x + 81” — correct.

---

11.

Expression:
3 + 2 + 5 + 7 + 2 + 3 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 + 5 + 2 +