Grade 5 Pre-Algebra worksheet focusing on solving two-step equations.

Problem: Solving Two-Step Equations

The task involves solving a series of two-step algebraic equations for the variable. Each equation requires isolating the variable through a combination of addition/subtraction and multiplication/division. Below, I will solve each equation step by step.

---

Equation 1: \( 10x - 75 = 754 \)

1. Add 75 to both sides:
\[
10x - 75 + 75 = 754 + 75
\]
\[
10x = 829
\]

2. Divide both sides by 10:
\[
x = \frac{829}{10}
\]
\[
x = 82.9
\]

Solution: \( x = 82.9 \)

---

Equation 2: \( 14y - 19 = 499 \)

1. Add 19 to both sides:
\[
14y - 19 + 19 = 499 + 19
\]
\[
14y = 518
\]

2. Divide both sides by 14:
\[
y = \frac{518}{14}
\]
\[
y = 37
\]

Solution: \( y = 37 \)

---

Equation 3: \( 11 + 55y = 2,981 \)

1. Subtract 11 from both sides:
\[
11 + 55y - 11 = 2,981 - 11
\]
\[
55y = 2,970
\]

2. Divide both sides by 55:
\[
y = \frac{2,970}{55}
\]
\[
y = 54
\]

Solution: \( y = 54 \)

---

Equation 4: \( 10z - 46 = 4 \)

1. Add 46 to both sides:
\[
10z - 46 + 46 = 4 + 46
\]
\[
10z = 50
\]

2. Divide both sides by 10:
\[
z = \frac{50}{10}
\]
\[
z = 5
\]

Solution: \( z = 5 \)

---

Equation 5: \( 40x + 42 = 1,162 \)

1. Subtract 42 from both sides:
\[
40x + 42 - 42 = 1,162 - 42
\]
\[
40x = 1,120
\]

2. Divide both sides by 40:
\[
x = \frac{1,120}{40}
\]
\[
x = 28
\]

Solution: \( x = 28 \)

---

Equation 6: \( 73 + 15x = 343 \)

1. Subtract 73 from both sides:
\[
73 + 15x - 73 = 343 - 73
\]
\[
15x = 270
\]

2. Divide both sides by 15:
\[
x = \frac{270}{15}
\]
\[
x = 18
\]

Solution: \( x = 18 \)

---

Equation 7: \( 2,528 - 72y = 8 \)

1. Subtract 2,528 from both sides:
\[
2,528 - 72y - 2,528 = 8 - 2,528
\]
\[
-72y = -2,520
\]

2. Divide both sides by -72:
\[
y = \frac{-2,520}{-72}
\]
\[
y = 35
\]

Solution: \( y = 35 \)

---

Equation 8: \( 81 + 68x = 1,849 \)

1. Subtract 81 from both sides:
\[
81 + 68x - 81 = 1,849 - 81
\]
\[
68x = 1,768
\]

2. Divide both sides by 68:
\[
x = \frac{1,768}{68}
\]
\[
x = 26
\]

Solution: \( x = 26 \)

---

Equation 9: \( 72y - 33 = 5,357 \)

1. Add 33 to both sides:
\[
72y - 33 + 33 = 5,357 + 33
\]
\[
72y = 5,390
\]

2. Divide both sides by 72:
\[
y = \frac{5,390}{72}
\]
\[
y = 74.8611 \quad (\text{or } y \approx 74.86 \text{ if rounding})
\]

Solution: \( y = \frac{5,390}{72} \) or \( y \approx 74.86 \)

---

Equation 10: \( 57z + 93 = 435 \)

1. Subtract 93 from both sides:
\[
57z + 93 - 93 = 435 - 93
\]
\[
57z = 342
\]

2. Divide both sides by 57:
\[
z = \frac{342}{57}
\]
\[
z = 6
\]

Solution: \( z = 6 \)

---

Equation 11: \( 13 + 33y = 274 \)

1. Subtract 13 from both sides:
\[
13 + 33y - 13 = 274 - 13
\]
\[
33y = 261
\]

2. Divide both sides by 33:
\[
y = \frac{261}{33}
\]
\[
y = 7.9091 \quad (\text{or } y \approx 7.91 \text{ if rounding})
\]

Solution: \( y = \frac{261}{33} \) or \( y \approx 7.91 \)

---

Equation 12: \( 77 + 82x = 7,867 \)

1. Subtract 77 from both sides:
\[
77 + 82x - 77 = 7,867 - 77
\]
\[
82x = 7,790
\]

2. Divide both sides by 82:
\[
x = \frac{7,790}{82}
\]
\[
x = 95
\]

Solution: \( x = 95 \)

---

Final Answers

\[
\boxed{
\begin{aligned}
1. & \ x = 82.9 \\
2. & \ y = 37 \\
3. & \ y = 54 \\
4. & \ z = 5 \\
5. & \ x = 28 \\
6. & \ x = 18 \\
7. & \ y = 35 \\
8. & \ x = 26 \\
9. & \ y = \frac{5,390}{72} \text{ or } y \approx 74.86 \\
10. & \ z = 6 \\
11. & \ y = \frac{261}{33} \text{ or } y \approx 7.91 \\
12. & \ x = 95 \\
\end{aligned}
}
\]