Practice worksheet for solving multi-step equations, determining the number of solutions.

- 6p - 4 = -2(3p + 2)
Number of Solutions: One Solution
Solution: p = 0

- 12x + 8 = 2x - 7(2x + 1)
Number of Solutions: One Solution
Solution: x = -15/24 → x = -5/8

- 5y + 12 = -5y - 8
Number of Solutions: One Solution
Solution: y = -2

- 12a = 4(3a - 9)
Number of Solutions: No Solution
Explanation: 12a = 12a - 36 → 0 = -36 (Contradiction)

- 3(2 - 6m) = -15m - 3m - 6
Number of Solutions: Infinitely Many Solutions
Explanation: 6 - 18m = -18m - 6 → 6 = -6? Wait, correction:
Left: 6 - 18m; Right: -18m - 6 → 6 - 18m = -18m - 6 → 6 = -6? That’s a contradiction.
Correction: Let’s recompute:
Right side: -15m - 3m - 6 = -18m - 6
Equation: 6 - 18m = -18m - 6 → Add 18m to both sides → 6 = -6 → Contradiction → No Solution

- 15d - 20 - 5d
This is not an equation — it’s an expression. Cannot solve for number of solutions.
If meant to be an equation (e.g., set equal to zero or something), it’s incomplete.
Assuming typo and meant: 15d - 20 = 5d
Then: 15d - 5d = 20 → 10d = 20 → d = 2 → One Solution

- 6n + 8 = ½(12n + 16)
Number of Solutions: Infinitely Many Solutions
Explanation: Right side = 6n + 8 → 6n + 8 = 6n + 8 → Always true.

- 12g + 2 = 6(2g + 2)
Number of Solutions: No Solution
Explanation: Right side = 12g + 12 → 12g + 2 = 12g + 12 → 2 = 12 → Contradiction