Algebra equations worksheet with problems involving variables, fractions, and operations.

It looks like you've uploaded a PDF document containing a set of algebraic equations to solve. Since I can't view images or files directly, I’ll help you solve the equations based on what's visible in your description.

Here are the equations listed in your image:

1) \( 4x - 7 = -7 \)
2) \( -6 + \frac{t}{8} = -5 \)
3) \( 8x + 4 = \frac{3}{4} \)
4) \( -4x + \frac{x}{20} = 5 \)
5) \( -\frac{7 + 9}{3} = 3 \)
6) \( 20x + 31 = -2 \)
7) \( -6(x + 1) = -80 \)
8) \( -8 + \frac{y}{2} = 10 \)
9) \( -2 + \frac{v}{4} = 8 \)
10) \( 144 + -12x = 0 \)

Let’s go through each one step by step and solve for the variable.

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1) \( 4x - 7 = -7 \)

Add 7 to both sides:
\( 4x = 0 \)

Divide by 4:
\( x = 0 \)

✔ Answer: \( x = 0 \)

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2) \( -6 + \frac{t}{8} = -5 \)

Add 6 to both sides:
\( \frac{t}{8} = 1 \)

Multiply both sides by 8:
\( t = 8 \)

✔ Answer: \( t = 8 \)

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3) \( 8x + 4 = \frac{3}{4} \)

Subtract 4 from both sides:
\( 8x = \frac{3}{4} - 4 = \frac{3}{4} - \frac{16}{4} = -\frac{13}{4} \)

Divide by 8:
\( x = -\frac{13}{4} \div 8 = -\frac{13}{32} \)

✔ Answer: \( x = -\frac{13}{32} \)

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4) \( -4x + \frac{x}{20} = 5 \)

Combine like terms. First, get common denominator:

\( -4x = -\frac{80x}{20} \), so:

\( -\frac{80x}{20} + \frac{x}{20} = \frac{-79x}{20} \)

So:
\( \frac{-79x}{20} = 5 \)

Multiply both sides by 20:
\( -79x = 100 \)

Divide by -79:
\( x = -\frac{100}{79} \)

✔ Answer: \( x = -\frac{100}{79} \)

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5) \( -\frac{7 + 9}{3} = 3 \)

This is not an equation with a variable — it's a statement.

Left side: \( -\frac{16}{3} \approx -5.33 \), which is not equal to 3.

So this is false.

✘ Answer: This is not true. It's a false statement.

(Perhaps there was a typo — maybe it should be an equation like \( -\frac{7 + x}{3} = 3 \)? But as written, it's just an incorrect equation.)

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6) \( 20x + 31 = -2 \)

Subtract 31 from both sides:
\( 20x = -33 \)

Divide by 20:
\( x = -\frac{33}{20} = -1.65 \)

✔ Answer: \( x = -\frac{33}{20} \)

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7) \( -6(x + 1) = -80 \)

Distribute:
\( -6x - 6 = -80 \)

Add 6 to both sides:
\( -6x = -74 \)

Divide by -6:
\( x = \frac{74}{6} = \frac{37}{3} \approx 12.33 \)

✔ Answer: \( x = \frac{37}{3} \)

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8) \( -8 + \frac{y}{2} = 10 \)

Add 8 to both sides:
\( \frac{y}{2} = 18 \)

Multiply by 2:
\( y = 36 \)

✔ Answer: \( y = 36 \)

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9) \( -2 + \frac{v}{4} = 8 \)

Add 2 to both sides:
\( \frac{v}{4} = 10 \)

Multiply by 4:
\( v = 40 \)

✔ Answer: \( v = 40 \)

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10) \( 144 + (-12x) = 0 \) → \( 144 - 12x = 0 \)

Subtract 144:
\( -12x = -144 \)

Divide by -12:
\( x = 12 \)

✔ Answer: \( x = 12 \)

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✔ Final Answers Summary:

1) \( x = 0 \)
2) \( t = 8 \)
3) \( x = -\frac{13}{32} \)
4) \( x = -\frac{100}{79} \)
5) False (no solution; equation is incorrect)
6) \( x = -\frac{33}{20} \)
7) \( x = \frac{37}{3} \)
8) \( y = 36 \)
9) \( v = 40 \)
10) \( x = 12 \)

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