Let's solve each problem step by step and evaluate the algebraic expressions for the given values of the variables.
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1. $ q - r - (-1) $ when $ q = 1, r = 7 $
$$
= 1 - 7 - (-1)
= 1 - 7 + 1
= -6 + 1 = \boxed{-5}
$$
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2. $ \frac{7x + 5}{-5} $ when $ x = -3 $
$$
= \frac{7(-3) + 5}{-5}
= \frac{-21 + 5}{-5}
= \frac{-16}{-5} = \boxed{\frac{16}{5}} \text{ or } \boxed{3.2}
$$
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3. $ q^3 - 3q + 12 $ at $ q = -5 $
$$
= (-5)^3 - 3(-5) + 12
= -125 + 15 + 12
= -125 + 27 = \boxed{-98}
$$
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4. $ \frac{c}{2} - 1 $ at $ c = 16 $
$$
= \frac{16}{2} - 1 = 8 - 1 = \boxed{7}
$$
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5. $ \frac{9v - 23}{5} $ at $ v = 7 $
$$
= \frac{9(7) - 23}{5}
= \frac{63 - 23}{5}
= \frac{40}{5} = \boxed{8}
$$
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6. $ (b^2 - 4b)^2 $ at $ b = -2 $
First compute inside the parentheses:
$$
b^2 = (-2)^2 = 4 \\
4b = 4(-2) = -8 \\
b^2 - 4b = 4 - (-8) = 4 + 8 = 12 \\
\text{Now square it: } (12)^2 = \boxed{144}
$$
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7. $ 6q(q + 7)^2 $ at $ q = -5 $
First compute $ q + 7 = -5 + 7 = 2 $, then square it:
$$
(2)^2 = 4 \\
6q = 6(-5) = -30 \\
\text{So: } -30 \times 4 = \boxed{-120}
$$
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8. $ \frac{4}{12 - 2y} + 3 $ at $ y = 5 $
$$
12 - 2(5) = 12 - 10 = 2 \\
\frac{4}{2} = 2 \\
2 + 3 = \boxed{5}
$$
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9. $ (y + 1)^4 $ at $ y = -2 $
$$
y + 1 = -2 + 1 = -1 \\
(-1)^4 = 1 \quad \text{(since even power)} \\
\boxed{1}
$$
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10. $ 5(k + 9) $ at $ k = -14 $
$$
k + 9 = -14 + 9 = -5 \\
5(-5) = \boxed{-25}
$$
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✔ Final Answers:
1. $ \boxed{-5} $
2. $ \boxed{\frac{16}{5}} $ or $ \boxed{3.2} $
3. $ \boxed{-98} $
4. $ \boxed{7} $
5. $ \boxed{8} $
6. $ \boxed{144} $
7. $ \boxed{-120} $
8. $ \boxed{5} $
9. $ \boxed{1} $
10. $ \boxed{-25} $
Let me know if you'd like these written out in a formatted worksheet!
Parent Tip: Review the logic above to help your child master the concept of solving algebraic expressions worksheet.
