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Linear equationsAlgebraMiddle schoolabout 0:53

Solve -6(x + 3) = -7x - 5: animated lesson

A narrated, step-by-step linear equations video lesson with captions. Final answer: x = 13.

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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
$-6~\left( x+3\right) = -7~ x-5$
2. Step by step
1. $-6~\left( x+3\right) = -7~ x-5$
  Start with the equation
2. $-6x - 18 = -7x - 5$
  Simplify each side (distribute and combine like terms)
3. $x - 18 = -5$
  Add 7x to both sides
4. $x = 13$
  Add 18 to both sides
3. On the graph
Each solution is where the graph of left side minus right side crosses zero.
4. The answer
$x = 13$
x = 13
5. Check
- x = 13: left side = -96, right side = -96 ✓

Transcript

The problem. Here is the problem: negative 6(x plus 3) equals negative 7x minus 5. 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 7x to both sides. Add 18 to both sides.

On the graph. Now look at the graph of the left side minus the right side. It crosses zero exactly at the solutions we found.

The answer. So the answer is x equals 13. Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

Check. x equals 13: left side equals negative 96, right side equals negative 96, which checks out.

About linear equations

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

Solve -6(x + 3) = -7x - 5: Animated Step-by-Step Lesson