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

Let's solve each problem step by step.

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Problem 1: Which of these expressions is equivalent to \(2(8x - 2)\)?

#### Solution:
We start by distributing the 2 across the terms inside the parentheses:
\[
2(8x - 2) = 2 \cdot 8x - 2 \cdot 2 = 16x - 4
\]

#### Answer:
The expression equivalent to \(2(8x - 2)\) is:
\[
\boxed{c}
\]

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Problem 2: Which of these expressions is not equivalent to \(2x^2\)?

#### Solution:
We analyze each option:

- Option a: \(2 \times x \times x\)
\[
2 \times x \times x = 2x^2
\]
This is equivalent to \(2x^2\).

- Option b: \(x^2 \times 2\)
\[
x^2 \times 2 = 2x^2
\]
This is equivalent to \(2x^2\).

- Option c: \(x \times 2 \times x\)
\[
x \times 2 \times x = 2x^2
\]
This is equivalent to \(2x^2\).

- Option d: \(x \times 2\)
\[
x \times 2 = 2x
\]
This is not equivalent to \(2x^2\).

#### Answer:
The expression that is not equivalent to \(2x^2\) is:
\[
\boxed{d}
\]

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Problem 3: Which of these expressions is equivalent to \(3(3x + 2x) + 30\)?

#### Solution:
First, simplify the expression inside the parentheses:
\[
3x + 2x = 5x
\]
So the expression becomes:
\[
3(5x) + 30 = 15x + 30
\]

Now, we compare this with the given options:

- Option a: \(3(5x) + 50\)
\[
3(5x) + 50 = 15x + 50
\]
This is not equivalent to \(15x + 30\).

- Option b: \(3(5x + 3)\)
\[
3(5x + 3) = 3 \cdot 5x + 3 \cdot 3 = 15x + 9
\]
This is not equivalent to \(15x + 30\).

- Option c: \(15x + 3\)
\[
15x + 3
\]
This is not equivalent to \(15x + 30\).

- Option d: \(3 + (3x + 2x)\)
\[
3 + (3x + 2x) = 3 + 5x
\]
This is not equivalent to \(15x + 30\).

None of the options match \(15x + 30\). However, if we recheck the problem, it seems there might be a typo in the options. Assuming the correct form is \(15x + 30\), the closest match is not listed. But based on the given options, none are correct.

#### Answer:
The expression equivalent to \(3(3x + 2x) + 30\) is:
\[
\boxed{\text{None}}
\]

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Problem 4: Which of these expressions is equivalent to \(-4(2x)\)?

#### Solution:
We distribute the \(-4\) across the term inside the parentheses:
\[
-4(2x) = -4 \cdot 2x = -8x
\]

#### Answer:
The expression equivalent to \(-4(2x)\) is:
\[
\boxed{a}
\]

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Problem 5: Which of these expressions is not equivalent to \(2c + c - 1 + c\)?

#### Solution:
First, simplify the given expression:
\[
2c + c - 1 + c = (2c + c + c) - 1 = 4c - 1
\]

Now, we compare this with the given options:

- Option a: \(4c + 10\)
\[
4c + 10
\]
This is not equivalent to \(4c - 1\).

- Option b: \(4c - 1\)
\[
4c - 1
\]
This is equivalent to \(4c - 1\).

- Option c: \(4c - c\)
\[
4c - c = 3c
\]
This is not equivalent to \(4c - 1\).

- Option d: \(-1 - 4c\)
\[
-1 - 4c
\]
This is not equivalent to \(4c - 1\).

Among these, the expression that is not equivalent to \(4c - 1\) is \(4c + 10\).

#### Answer:
The expression that is not equivalent to \(2c + c - 1 + c\) is:
\[
\boxed{a}
\]

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Problem 6: Which of these expressions is equivalent to \(\frac{-4v}{c^2}\)?

#### Solution:
We analyze each option:

- Option a: \(\frac{-2(2v)}{c}\)
\[
\frac{-2(2v)}{c} = \frac{-4v}{c}
\]
This is not equivalent to \(\frac{-4v}{c^2}\).

- Option b: \(\frac{-2(2v)}{c^2}\)
\[
\frac{-2(2v)}{c^2} = \frac{-4v}{c^2}
\]
This is equivalent to \(\frac{-4v}{c^2}\).

- Option c: \(\frac{-4v}{2c}\)
\[
\frac{-4v}{2c} = \frac{-2v}{c}
\]
This is not equivalent to \(\frac{-4v}{c^2}\).

- Option d: \(\frac{2}{c} \times \frac{2v}{c}\)
\[
\frac{2}{c} \times \frac{2v}{c} = \frac{2 \cdot 2v}{c \cdot c} = \frac{4v}{c^2}
\]
This is not equivalent to \(\frac{-4v}{c^2}\).

#### Answer:
The expression equivalent to \(\frac{-4v}{c^2}\) is:
\[
\boxed{b}
\]

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Final Answers:

1. \(\boxed{c}\)
2. \(\boxed{d}\)
3. \(\boxed{\text{None}}\)
4. \(\boxed{a}\)
5. \(\boxed{a}\)
6. \(\boxed{b}\)

\boxed{c, d, \text{None}, a, a, b}