Pre Algebra Equations worksheet with five problems to solve using inverse operations.

Looking at the worksheet, I need to solve five pre-algebra equations for the variable y. Each equation has a similar structure: (y² + constant) - coefficient × (expression with y) = result.

Let me solve each one step by step:

Problem 1: (y² + 9) - 6×(4 + y) = -23

First, distribute the -6:
y² + 9 - 24 - 6y = -23

Combine like terms:
y² - 6y - 15 = -23

Add 23 to both sides:
y² - 6y + 8 = 0

Factor:
(y - 2)(y - 4) = 0

So y = 2 or y = 4

Problem 2: (y² + 4) - 12×(12 + y) = -151

Distribute the -12:
y² + 4 - 144 - 12y = -151

Combine like terms:
y² - 12y - 140 = -151

Add 151 to both sides:
y² - 12y + 11 = 0

Factor:
(y - 1)(y - 11) = 0

So y = 1 or y = 11

Problem 3: (y² + 4) - 12×(2 + y) = -40

Distribute the -12:
y² + 4 - 24 - 12y = -40

Combine like terms:
y² - 12y - 20 = -40

Add 40 to both sides:
y² - 12y + 20 = 0

Factor:
(y - 2)(y - 10) = 0

So y = 2 or y = 10

Problem 4: (y² + 10) - 4×(10 + y) = 66

Distribute the -4:
y² + 10 - 40 - 4y = 66

Combine like terms:
y² - 4y - 30 = 66

Add 30 to both sides:
y² - 4y - 96 = 0

Factor:
(y - 12)(y + 8) = 0

So y = 12 or y = -8

Problem 5: (y² + 7) - 3×(2 + y) = 109

Distribute the -3:
y² + 7 - 6 - 3y = 109

Combine like terms:
y² - 3y + 1 = 109

Subtract 109 from both sides:
y² - 3y - 108 = 0

Factor:
(y - 12)(y + 9) = 0

So y = 12 or y = -9

Final Answer:
1. y = 2 or y = 4
2. y = 1 or y = 11
3. y = 2 or y = 10
4. y = 12 or y = -8
5. y = 12 or y = -9