To solve the given algebraic expressions, we will substitute the provided values for each variable and simplify step by step. Let's go through each section:
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Section 1: Evaluate the following expressions for \( x = 4 \)
1. \( x + 8 \)
\[
x + 8 = 4 + 8 = 12
\]
2. \( 2x - 1 \)
\[
2x - 1 = 2(4) - 1 = 8 - 1 = 7
\]
3. \( 10 + x^2 \)
\[
10 + x^2 = 10 + 4^2 = 10 + 16 = 26
\]
4. \( -x - 12 \)
\[
-x - 12 = -(4) - 12 = -4 - 12 = -16
\]
5. \( -4 + x^2 \)
\[
-4 + x^2 = -4 + 4^2 = -4 + 16 = 12
\]
6. \( x^2 - 1 \)
\[
x^2 - 1 = 4^2 - 1 = 16 - 1 = 15
\]
---
Section 2: Evaluate the following expressions for \( y = -2 \)
1. \( 3y - 3 \)
\[
3y - 3 = 3(-2) - 3 = -6 - 3 = -9
\]
2. \( -2y - 16 \)
\[
-2y - 16 = -2(-2) - 16 = 4 - 16 = -12
\]
3. \( 16 + y^2 \)
\[
16 + y^2 = 16 + (-2)^2 = 16 + 4 = 20
\]
4. \( -2y + 20 \)
\[
-2y + 20 = -2(-2) + 20 = 4 + 20 = 24
\]
5. \( y^2 + 12 \)
\[
y^2 + 12 = (-2)^2 + 12 = 4 + 12 = 16
\]
6. \( -y^2 - 20 \)
\[
-y^2 - 20 = -(-2)^2 - 20 = -4 - 20 = -24
\]
---
Section 3: Evaluate the following expressions for \( t = -5 \)
1. \( t^2 + 75 \)
\[
t^2 + 75 = (-5)^2 + 75 = 25 + 75 = 100
\]
2. \( -t - 25 \)
\[
-t - 25 = -(-5) - 25 = 5 - 25 = -20
\]
3. \( -t + 10 \)
\[
-t + 10 = -(-5) + 10 = 5 + 10 = 15
\]
4. \( 22 - 2t \)
\[
22 - 2t = 22 - 2(-5) = 22 + 10 = 32
\]
5. \( -4t - 5 \)
\[
-4t - 5 = -4(-5) - 5 = 20 - 5 = 15
\]
6. \( -t - 10 \)
\[
-t - 10 = -(-5) - 10 = 5 - 10 = -5
\]
---
Section 4: Evaluate the following expressions for \( q = -1 \)
1. \( 12 + q^2 \)
\[
12 + q^2 = 12 + (-1)^2 = 12 + 1 = 13
\]
2. \( -q^2 - q \)
\[
-q^2 - q = -(-1)^2 - (-1) = -1 + 1 = 0
\]
3. \( q + 2q \)
\[
q + 2q = -1 + 2(-1) = -1 - 2 = -3
\]
4. \( -2q - 30 \)
\[
-2q - 30 = -2(-1) - 30 = 2 - 30 = -28
\]
5. \( -q - 2q \)
\[
-q - 2q = -(-1) - 2(-1) = 1 + 2 = 3
\]
6. \( 3q^2 - 3 \)
\[
3q^2 - 3 = 3(-1)^2 - 3 = 3(1) - 3 = 3 - 3 = 0
\]
---
Section 5: Evaluate the following expressions for \( s = -3 \)
1. \( s^2 \)
\[
s^2 = (-3)^2 = 9
\]
2. \( 2s - 1 \)
\[
2s - 1 = 2(-3) - 1 = -6 - 1 = -7
\]
3. \( s + s^3 \)
\[
s + s^3 = -3 + (-3)^3 = -3 + (-27) = -3 - 27 = -30
\]
4. \( s + (-1) \)
\[
s + (-1) = -3 + (-1) = -3 - 1 = -4
\]
5. \( -s + 27 \)
\[
-s + 27 = -(-3) + 27 = 3 + 27 = 30
\]
6. \( s^2 - 1 \)
\[
s^2 - 1 = (-3)^2 - 1 = 9 - 1 = 8
\]
---
Final Answers
1. For \( x = 4 \):
\[
\boxed{12, 7, 26, -16, 12, 15}
\]
2. For \( y = -2 \):
\[
\boxed{-9, -12, 20, 24, 16, -24}
\]
3. For \( t = -5 \):
\[
\boxed{100, -20, 15, 32, 15, -5}
\]
4. For \( q = -1 \):
\[
\boxed{13, 0, -3, -28, 3, 0}
\]
5. For \( s = -3 \):
\[
\boxed{9, -7, -30, -4, 30, 8}
\]
Parent Tip: Review the logic above to help your child master the concept of algebraic expressions worksheet pdf.
