7th Grade Algebraic Expressions Worksheets - Math Monks - Free Printable

Here's the step-by-step solution for each of the 10 problems on the worksheet.

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Problem 1.
Evaluate:
> $\frac{3}{s - t} - 1$ at $s = 2$, $t = -6$

Step 1: Substitute values:
$\frac{3}{2 - (-6)} - 1 = \frac{3}{2 + 6} - 1 = \frac{3}{8} - 1$

Step 2: Convert 1 to eighths:
$\frac{3}{8} - \frac{8}{8} = -\frac{5}{8}$

✔ Answer: $-\frac{5}{8}$

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Problem 2.
Evaluate:
> $\frac{x + 1}{y^2}$ at $x = 8$, $y = \frac{3}{5}$

Step 1: Substitute values:
$\frac{8 + 1}{\left(\frac{3}{5}\right)^2} = \frac{9}{\frac{9}{25}}$

Step 2: Divide fractions:
$9 \div \frac{9}{25} = 9 \times \frac{25}{9} = 25$

✔ Answer: $25$

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Problem 3.
Evaluate:
> $\frac{3}{u}(u^2 + 68)$ at $u = -12$

Step 1: Substitute value:
$\frac{3}{-12}((-12)^2 + 68) = -\frac{1}{4}(144 + 68)$

Step 2: Simplify inside parentheses:
$-\frac{1}{4}(212) = -53$

✔ Answer: $-53$

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Problem 4.
Evaluate:
> $21r(63r + 3)$ at $r = -\frac{3}{7}$

Step 1: Substitute value:
$21 \cdot \left(-\frac{3}{7}\right) \cdot \left(63 \cdot \left(-\frac{3}{7}\right) + 3\right)$

Step 2: Simplify each part:
$21 \cdot -\frac{3}{7} = -9$
$63 \cdot -\frac{3}{7} = -27$ → so inside: $-27 + 3 = -24$

Step 3: Multiply:
$-9 \cdot (-24) = 216$

✔ Answer: $216$

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Problem 5.
Evaluate:
> $6n^2 + 4n^2 - 19$ at $n = -3$

Step 1: Combine like terms first:
$(6 + 4)n^2 - 19 = 10n^2 - 19$

Step 2: Substitute $n = -3$:
$10(-3)^2 - 19 = 10(9) - 19 = 90 - 19 = 71$

✔ Answer: $71$

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Problem 6.
Evaluate:
> $\frac{12q - 34}{4}$ at $q = -\frac{1}{3}$

Step 1: Substitute value:
$\frac{12 \cdot (-\frac{1}{3}) - 34}{4} = \frac{-4 - 34}{4} = \frac{-38}{4}$

Step 2: Simplify fraction:
$-\frac{38}{4} = -\frac{19}{2} = -9.5$

✔ Answer: $-\frac{19}{2}$ or $-9.5$

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Problem 7.
Evaluate:
> $\frac{5t}{3t - s} - 1$ at $s = 2$, $t = -6$

Step 1: Substitute values:
$\frac{5(-6)}{3(-6) - 2} - 1 = \frac{-30}{-18 - 2} - 1 = \frac{-30}{-20} - 1$

Step 2: Simplify:
$\frac{-30}{-20} = \frac{3}{2}$, so:
$\frac{3}{2} - 1 = \frac{1}{2}$

✔ Answer: $\frac{1}{2}$

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Problem 8.
Evaluate:
> $\frac{s - 4}{t^2}$ at $s = 5$, $t = -5$

Step 1: Substitute values:
$\frac{5 - 4}{(-5)^2} = \frac{1}{25}$

✔ Answer: $\frac{1}{25}$

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Problem 9.
Evaluate:
> $\frac{6q - g}{4}$ at $q = -4$, $g = 1$

Step 1: Substitute values:
$\frac{6(-4) - 1}{4} = \frac{-24 - 1}{4} = \frac{-25}{4}$

✔ Answer: $-\frac{25}{4}$

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Problem 10.
Evaluate:
> $(10p - 4)^2$ at $p = 2$

Step 1: Substitute value:
$(10 \cdot 2 - 4)^2 = (20 - 4)^2 = 16^2 = 256$

✔ Answer: $256$

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## ✔ Final Answers:

1. $-\frac{5}{8}$
2. $25$
3. $-53$
4. $216$
5. $71$
6. $-\frac{19}{2}$
7. $\frac{1}{2}$
8. $\frac{1}{25}$
9. $-\frac{25}{4}$
10. $256$

Let me know if you'd like these written in a boxed format or need further explanation!