Algebra equations worksheet for practice.

It looks like you've uploaded a worksheet with a set of equations to solve for the variable \( x \). The instructions at the top say: "Solve for \( x \). Use the correct method for each one."

Let’s go through each equation step by step and solve them.

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1.)

\( 15 + 6x + 2x = 18 \)

Combine like terms:
\[
15 + 8x = 18
\]

Subtract 15 from both sides:
\[
8x = 3
\]

Divide by 8:
\[
x = \frac{3}{8}
\]

✔ Answer: \( x = \frac{3}{8} \)

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2.)

\( 26 = 2x + 5x + 6 \)

Combine like terms on the right:
\[
26 = 7x + 6
\]

Subtract 6 from both sides:
\[
20 = 7x
\]

Divide by 7:
\[
x = \frac{20}{7}
\]

✔ Answer: \( x = \frac{20}{7} \)

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3.)

\( 4x + 10 + 3x = 52 \)

Combine like terms:
\[
7x + 10 = 52
\]

Subtract 10:
\[
7x = 42
\]

Divide by 7:
\[
x = 6
\]

✔ Answer: \( x = 6 \)

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4.)

\( 77 = x + 7x + 8 \)

Combine like terms:
\[
77 = 8x + 8
\]

Subtract 8:
\[
69 = 8x
\]

Divide by 8:
\[
x = \frac{69}{8} = 8.625
\]

✔ Answer: \( x = \frac{69}{8} \) or \( 8.625 \)

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5.)

\( 7x + 9 = 3x + 15 \)

Move all \( x \)-terms to one side, constants to the other:

Subtract \( 3x \) from both sides:
\[
4x + 9 = 15
\]

Subtract 9:
\[
4x = 6
\]

Divide by 4:
\[
x = \frac{6}{4} = \frac{3}{2} = 1.5
\]

✔ Answer: \( x = \frac{3}{2} \)

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6.)

\( 2x - 4 = 2x + 24 \)

Subtract \( 2x \) from both sides:
\[
-4 = 24
\]

✘ This is not true, so there is no solution.

✔ Answer: No solution (contradiction)

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7.)

\( 126 = 4x + 7x + 3 \)

Combine like terms:
\[
126 = 11x + 3
\]

Subtract 3:
\[
123 = 11x
\]

Divide by 11:
\[
x = \frac{123}{11} \approx 11.18
\]

✔ Answer: \( x = \frac{123}{11} \)

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8.)

\( 9 + 4x = x + 14 \)

Subtract \( x \) from both sides:
\[
9 + 3x = 14
\]

Subtract 9:
\[
3x = 5
\]

Divide by 3:
\[
x = \frac{5}{3} \approx 1.67
\]

✔ Answer: \( x = \frac{5}{3} \)

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9.)

\( 4 + 7x = 36 \)

Subtract 4:
\[
7x = 32
\]

Divide by 7:
\[
x = \frac{32}{7} \approx 4.57
\]

✔ Answer: \( x = \frac{32}{7} \)

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10.)

\( 62 = 3x + 2x + 2 \)

Combine like terms:
\[
62 = 5x + 2
\]

Subtract 2:
\[
60 = 5x
\]

Divide by 5:
\[
x = 12
\]

✔ Answer: \( x = 12 \)

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11.)

\( 48 = 3x + x + 8 \)

Combine like terms:
\[
48 = 4x + 8
\]

Subtract 8:
\[
40 = 4x
\]

Divide by 4:
\[
x = 10
\]

✔ Answer: \( x = 10 \)

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12.)

\( 88 = 3x + 5x + 8 \)

Combine like terms:
\[
88 = 8x + 8
\]

Subtract 8:
\[
80 = 8x
\]

Divide by 8:
\[
x = 10
\]

✔ Answer: \( x = 10 \)

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1.) | \( x = \frac{3}{8} \) |
| 2.) | \( x = \frac{20}{7} \) |
| 3.) | \( x = 6 \) |
| 4.) | \( x = \frac{69}{8} \) |
| 5.) | \( x = \frac{3}{2} \) |
| 6.) | No solution |
| 7.) | \( x = \frac{123}{11} \) |
| 8.) | \( x = \frac{5}{3} \) |
| 9.) | \( x = \frac{32}{7} \) |
| 10.) | \( x = 12 \) |
| 11.) | \( x = 10 \) |
| 12.) | \( x = 10 \) |

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