This worksheet helps students practice substituting values into algebraic expressions for variables like x, y, t, q, and s.

Let's solve each expression step by step, substituting the given values for the variables.

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Part 1: Evaluate for $ x = 4 $

1) $ x + 8 = 4 + 8 = \boxed{12} $

2) $ 2x - 1 = 2(4) - 1 = 8 - 1 = \boxed{7} $

3) $ 10 + x^2 = 10 + (4)^2 = 10 + 16 = \boxed{26} $

4) $ -x - 12 = -(4) - 12 = -4 - 12 = \boxed{-16} $

5) $ -4 + x^2 = -4 + (4)^2 = -4 + 16 = \boxed{12} $

6) $ x^2 - 1 = (4)^2 - 1 = 16 - 1 = \boxed{15} $

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Part 2: Evaluate for $ y = -2 $

1) $ 3y - 3 = 3(-2) - 3 = -6 - 3 = \boxed{-9} $

2) $ -2y - 16 = -2(-2) - 16 = 4 - 16 = \boxed{-12} $

3) $ 16 + y^2 = 16 + (-2)^2 = 16 + 4 = \boxed{20} $

4) $ -2y + 20 = -2(-2) + 20 = 4 + 20 = \boxed{24} $

5) $ y^2 + 12 = (-2)^2 + 12 = 4 + 12 = \boxed{16} $

6) $ -y^2 - 20 = -(-2)^2 - 20 = -(4) - 20 = -4 - 20 = \boxed{-24} $

> Note: $-y^2$ means $-(y^2)$, not $(-y)^2$. So we square first, then apply the negative.

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Part 3: Evaluate for $ t = -5 $

1) $ t^2 + 75 = (-5)^2 + 75 = 25 + 75 = \boxed{100} $

2) $ -t - 25 = -(-5) - 25 = 5 - 25 = \boxed{-20} $

3) $ -t + 10 = -(-5) + 10 = 5 + 10 = \boxed{15} $

4) $ 22 - 2t = 22 - 2(-5) = 22 + 10 = \boxed{32} $

5) $ -4t - 5 = -4(-5) - 5 = 20 - 5 = \boxed{15} $

6) $ -t - 10 = -(-5) - 10 = 5 - 10 = \boxed{-5} $

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Part 4: Evaluate for $ q = -1 $

1) $ 12 + q^2 = 12 + (-1)^2 = 12 + 1 = \boxed{13} $

2) $ -q^2 - q = -(-1)^2 - (-1) = -(1) + 1 = -1 + 1 = \boxed{0} $

3) $ q + 2q = (-1) + 2(-1) = -1 - 2 = \boxed{-3} $

4) $ -2q - 30 = -2(-1) - 30 = 2 - 30 = \boxed{-28} $

5) $ -q - 2q = -(-1) - 2(-1) = 1 + 2 = \boxed{3} $

6) $ 3q^2 - 3 = 3(-1)^2 - 3 = 3(1) - 3 = 3 - 3 = \boxed{0} $

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Part 5: Evaluate for $ s = -3 $

1) $ s^2 = (-3)^2 = \boxed{9} $

2) $ 2s - 1 = 2(-3) - 1 = -6 - 1 = \boxed{-7} $

3) $ s + s^3 = (-3) + (-3)^3 = -3 + (-27) = -3 - 27 = \boxed{-30} $

4) $ s + (-1) = -3 + (-1) = -3 - 1 = \boxed{-4} $

5) $ -s + 27 = -(-3) + 27 = 3 + 27 = \boxed{30} $

6) $ s^2 - 1 = (-3)^2 - 1 = 9 - 1 = \boxed{8} $

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✔ Final Answers:

#### For $ x = 4 $:
1) 12
2) 7
3) 26
4) -16
5) 12
6) 15

#### For $ y = -2 $:
1) -9
2) -12
3) 20
4) 24
5) 16
6) -24

#### For $ t = -5 $:
1) 100
2) -20
3) 15
4) 32
5) 15
6) -5

#### For $ q = -1 $:
1) 13
2) 0
3) -3
4) -28
5) 3
6) 0

#### For $ s = -3 $:
1) 9
2) -7
3) -30
4) -4
5) 30
6) 8

Let me know if you'd like this formatted as a completed worksheet!