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InequalitiesAlgebraHigh schoolabout 0:55

Solve |x + 5| >= 0: animated lesson

A narrated, step-by-step inequalities video lesson with captions. Final answer: All real numbers; interval notation: (−∞, ∞).

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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 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$|x + 5| \ge 0$
2. Step by step
1. $|x + 5| \ge 0$
  Write the problem with the absolute value isolated
2. $0 = 0$
  Compare the right-hand side with zero
3. $(-\infty,\ \infty)$
  Write the solution set in interval notation
3. The answer
$x \in \mathbb{R} \qquad (-\infty,\ \infty)$
|x + 5| ≥ 0 → All real numbers

Transcript

The problem. Here is the problem: |x plus 5| greater than or equal to 0. Solve an absolute value inequality by turning it into a compound inequality and finding the boundary points.

Step by step. Write the problem with the absolute value isolated. The absolute value is already alone on one side, so it can be split into cases. Compare the right-hand side with zero. An absolute value is always at least 0, so it is greater than (or equal to) any negative number, and at least 0 everywhere. Write the solution set in interval notation.

The answer. So the answer is All real numbers; interval notation: (−∞, ∞). An absolute value inequality compares a distance with c: "less than" keeps the inside within c of zero (one interval), "greater than" pushes it beyond c (two rays).

About inequalities

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

Solve |x + 5| >= 0: Inequalities Step-by-Step Lesson