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Linear equationsAlgebraMiddle schoolabout 0:51

Solve (x - 1)/6 + (x - 8)/6 = 8: animated lesson

A narrated, step-by-step linear equations video lesson with captions. Final answer: x = 57/2 ≈ 28.5.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Solving an equation
$\frac{ x-1}{6}+\frac{ x-8}{6} = 8$
2. Step by step
1. $\frac{ x-1}{6}+\frac{ x-8}{6} = 8$
  Start with the equation
2. $\frac{1}{3}x - \frac{3}{2} = 8$
  Simplify each side (distribute and combine like terms)
3. $\frac{1}{3}x = \frac{19}{2}$
  Add 3/2 to both sides
4. $x = \frac{19}{2} \div \frac{1}{3} = \frac{57}{2}$
  Divide both sides by 1/3 (multiply by its reciprocal)
3. The answer
$x = \frac{57}{2} \approx 28.5$
x = 57/2 ≈ 28.5
4. Check
- x = 28.5: left side = 8, right side = 8 ✓

Transcript

The problem. Here is the problem: (x minus 1)/6 plus (x minus 8)/6 equals 8. A linear equation in x: isolate x using inverse operations.

Step by step. Start with the equation. Simplify each side (distribute and combine like terms). Add 3 over 2 to both sides. Divide both sides by 1 over 3 (multiply by its reciprocal).

The answer. So the answer is x equals 57 over 2 approximately 28.5. Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

Check. x equals 28.5: left side equals 8, right side equals 8, which checks out.

About linear equations

Solve one-variable linear equations, including ones with brackets and fractions, and check the solution.

Solve (x - 1)/6 + (x - 8)/6 = 8: Linear equations Lesson