Solving Literal Equations “Connect 4” Activity {Student Approved ... - Free Printable

Let's solve each equation step by step, isolating the variable we're solving for. I'll go through each one in order.

---

1. $ 3x + y = z $ — Solve for $ x $

Step 1: Subtract $ y $ from both sides:
$$
3x = z - y
$$

Step 2: Divide both sides by 3:
$$
x = \frac{z - y}{3}
$$

✔ Answer: $ x = \frac{z - y}{3} $

---

2. $ ab + d = c + e $ — Solve for $ a $

Step 1: Subtract $ d $ from both sides:
$$
ab = c + e - d
$$

Step 2: Divide both sides by $ b $ (assuming $ b \neq 0 $):
$$
a = \frac{c + e - d}{b}
$$

✔ Answer: $ a = \frac{c + e - d}{b} $

---

3. $ P = 4c $ — Solve for $ c $

Step 1: Divide both sides by 4:
$$
c = \frac{P}{4}
$$

✔ Answer: $ c = \frac{P}{4} $

---

4. $ 24 = lwh $ — Solve for $ w $

Step 1: Divide both sides by $ lh $ (assuming $ l \neq 0, h \neq 0 $):
$$
w = \frac{24}{lh}
$$

✔ Answer: $ w = \frac{24}{lh} $

---

5. $ q + ad = m $ — Solve for $ d $

Step 1: Subtract $ q $ from both sides:
$$
ad = m - q
$$

Step 2: Divide both sides by $ a $ (assuming $ a \neq 0 $):
$$
d = \frac{m - q}{a}
$$

✔ Answer: $ d = \frac{m - q}{a} $

---

6. $ fd - m = 8 $ — Solve for $ d $

Step 1: Add $ m $ to both sides:
$$
fd = 8 + m
$$

Step 2: Divide both sides by $ f $ (assuming $ f \neq 0 $):
$$
d = \frac{8 + m}{f}
$$

✔ Answer: $ d = \frac{8 + m}{f} $

---

7. $ Ac - 10 = h $ — Solve for $ c $

Step 1: Add 10 to both sides:
$$
Ac = h + 10
$$

Step 2: Divide both sides by $ A $ (assuming $ A \neq 0 $):
$$
c = \frac{h + 10}{A}
$$

✔ Answer: $ c = \frac{h + 10}{A} $

---

8. $ P = 2(l + w) $ — Solve for $ w $

Step 1: Divide both sides by 2:
$$
\frac{P}{2} = l + w
$$

Step 2: Subtract $ l $ from both sides:
$$
w = \frac{P}{2} - l
$$

✔ Answer: $ w = \frac{P}{2} - l $

---

9. $ 2g - 4f = 6f $ — Solve for $ g $

Step 1: Add $ 4f $ to both sides:
$$
2g = 6f + 4f = 10f
$$

Step 2: Divide both sides by 2:
$$
g = 5f
$$

✔ Answer: $ g = 5f $

---

10. $ nxz - f = 3f $ — Solve for $ x $

Step 1: Add $ f $ to both sides:
$$
nxz = 3f + f = 4f
$$

Step 2: Divide both sides by $ nz $ (assuming $ n \neq 0, z \neq 0 $):
$$
x = \frac{4f}{nz}
$$

✔ Answer: $ x = \frac{4f}{nz} $

---

11. $ 4d - p = m $ — Solve for $ d $

Step 1: Add $ p $ to both sides:
$$
4d = m + p
$$

Step 2: Divide both sides by 4:
$$
d = \frac{m + p}{4}
$$

✔ Answer: $ d = \frac{m + p}{4} $

---

12. $ \frac{1}{5}v + gt = a $ — Solve for $ v $

Step 1: Subtract $ gt $ from both sides:
$$
\frac{1}{5}v = a - gt
$$

Step 2: Multiply both sides by 5:
$$
v = 5(a - gt)
$$

✔ Answer: $ v = 5(a - gt) $

---

13. $ D = rt $ — Solve for $ t $

Step 1: Divide both sides by $ r $ (assuming $ r \neq 0 $):
$$
t = \frac{D}{r}
$$

✔ Answer: $ t = \frac{D}{r} $

---

14. $ 2wy - 8n = 4k $ — Solve for $ w $

Step 1: Add $ 8n $ to both sides:
$$
2wy = 4k + 8n
$$

Step 2: Divide both sides by $ 2y $ (assuming $ y \neq 0 $):
$$
w = \frac{4k + 8n}{2y} = \frac{2k + 4n}{y}
$$

✔ Answer: $ w = \frac{2k + 4n}{y} $

---

15. $ 8rs - 8s = 16p $ — Solve for $ r $

Step 1: Factor out $ 8s $ on the left:
$$
8s(r - 1) = 16p
$$

Step 2: Divide both sides by $ 8s $ (assuming $ s \neq 0 $):
$$
r - 1 = \frac{16p}{8s} = \frac{2p}{s}
$$

Step 3: Add 1 to both sides:
$$
r = \frac{2p}{s} + 1
$$

✔ Answer: $ r = \frac{2p}{s} + 1 $

---

16. $ bg + 9f = 27 $ — Solve for $ g $

Step 1: Subtract $ 9f $ from both sides:
$$
bg = 27 - 9f
$$

Step 2: Divide both sides by $ b $ (assuming $ b \neq 0 $):
$$
g = \frac{27 - 9f}{b}
$$

✔ Answer: $ g = \frac{27 - 9f}{b} $

---

✔ Final Answers Summary:

| Equation | Variable Solved For | Solution |
|--------|---------------------|---------|
| $ 3x + y = z $ | $ x $ | $ x = \frac{z - y}{3} $ |
| $ ab + d = c + e $ | $ a $ | $ a = \frac{c + e - d}{b} $ |
| $ P = 4c $ | $ c $ | $ c = \frac{P}{4} $ |
| $ 24 = lwh $ | $ w $ | $ w = \frac{24}{lh} $ |
| $ q + ad = m $ | $ d $ | $ d = \frac{m - q}{a} $ |
| $ fd - m = 8 $ | $ d $ | $ d = \frac{8 + m}{f} $ |
| $ Ac - 10 = h $ | $ c $ | $ c = \frac{h + 10}{A} $ |
| $ P = 2(l + w) $ | $ w $ | $ w = \frac{P}{2} - l $ |
| $ 2g - 4f = 6f $ | $ g $ | $ g = 5f $ |
| $ nxz - f = 3f $ | $ x $ | $ x = \frac{4f}{nz} $ |
| $ 4d - p = m $ | $ d $ | $ d = \frac{m + p}{4} $ |
| $ \frac{1}{5}v + gt = a $ | $ v $ | $ v = 5(a - gt) $ |
| $ D = rt $ | $ t $ | $ t = \frac{D}{r} $ |
| $ 2wy - 8n = 4k $ | $ w $ | $ w = \frac{2k + 4n}{y} $ |
| $ 8rs - 8s = 16p $ | $ r $ | $ r = \frac{2p}{s} + 1 $ |
| $ bg + 9f = 27 $ | $ g $ | $ g = \frac{27 - 9f}{b} $ |

Let me know if you'd like these written in LaTeX format or need help with any specific steps!