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InequalitiesAlgebraHigh schoolabout 1:15

Solve -2x - 6 >= -6: animated lesson

A narrated, step-by-step inequalities video lesson with captions. Final answer: (-∞, 0].

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Transcript

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 (0.4 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$-2x-6 \ge -6$
2. Step by step
1. $x \le 0$
  Move everything to one side and isolate the variable
2. Test one point in each interval (sign chart)
3. Decide the endpoints
4. $x \in (-\infty, 0]$
  Write the solution set
3. The answer
$(-\infty, 0]$
x ∈ (-∞, 0]
4. Check
- x = -1: satisfies the inequality.
- x = 1: does not satisfy the inequality.

Transcript

The problem. Here is the problem: negative 2x minus 6 greater than equals negative 6. Solve the inequality and give the answer in interval notation.

Step by step. Move everything to one side and isolate the variable. Collect terms: negative 2x greater than or equal to 0. Dividing by a negative coefficient reverses the inequality sign. Test one point in each interval (sign chart). (-∞, 0): test x equals negative 1 → sign plus → included; (0, ∞): test x equals 1 → sign minus → excluded. Decide the endpoints. 0: included (the expression equals 0 and the sign allows equality). Write the solution set.

The answer. So the answer is (-∞, 0]. The inequality holds exactly for x in (-∞, 0]. Points where the expression is undefined are never included, and endpoints are included only for less than or equal to or greater than or equal to where the expression equals zero.

Check. x equals negative 1: satisfies the inequality. x equals 1: does not satisfy the inequality.

About inequalities

Solve linear and quadratic inequalities and write the answer as an interval.

Solve -2x - 6 >= -6: Inequalities Step-by-Step Lesson