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Linear equationsAlgebraMiddle schoolabout 0:58

Solve 2/3 x + 1/2 = 5/6: animated lesson

A narrated, step-by-step linear equations video lesson with captions. Final answer: x = 1/2 ≈ 0.5.

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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
$\frac{2}{3}~ x+\frac{1}{2} = \frac{5}{6}$
2. Step by step
1. $\frac{2}{3}~ x+\frac{1}{2} = \frac{5}{6}$
  Start with the equation
2. $\frac{2}{3}x + \frac{1}{2} = \frac{5}{6}$
  Simplify each side (distribute and combine like terms)
3. $\frac{2}{3}x = \frac{1}{3}$
  Subtract 1/2 from both sides
4. $x = \frac{1}{3} \div \frac{2}{3} = \frac{1}{2}$
  Divide both sides by 2/3 (multiply by its reciprocal)
3. The answer
$x = \frac{1}{2} \approx 0.5$
x = 1/2 ≈ 0.5
4. Check
- x = 0.5: left side = 0.83333333, right side = 0.83333333 ✓

Transcript

The problem. Here is the problem: 2 over 3 x plus 1 over 2 equals 5 over 6. 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). Subtract 1 over 2 from both sides. Divide both sides by 2 over 3 (multiply by its reciprocal).

The answer. So the answer is x equals 1 over 2 approximately 0.5. Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

Check. x equals 0.5: left side equals 0.83333333, right side equals 0.83333333, which checks out.

About linear equations

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

Solve 2/3 x + 1/2 = 5/6: Animated Step-by-Step Lesson