Solve a problem

InequalitiesAlgebraHigh schoolabout 0:59

Solve x^2 < 0: animated lesson

A narrated, step-by-step inequalities video lesson with captions. Final answer: No solution (∅).

SpeedLanguage

Chapters

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
${x}^{2} < 0$
2. Steps, part 1
1. $x^{2} < 0$
  Move everything to one side and factor
2. Find the critical points
3. Test one point in each interval (sign chart)
4. Decide the endpoints
3. Steps, part 2
1. $x \in \varnothing$
  Write the solution set
4. The answer
$\varnothing$
x ∈ No solution (∅)
5. Check
- x = -1: does not satisfy the inequality.
- x = 1: does not satisfy the inequality.

Transcript

The problem. Here is the problem: x squared less than 0. Solve the inequality and give the answer in interval notation.

Steps, part 1. Move everything to one side and factor. A sign chart needs the form f(x) compared with 0, written as a product/quotient of factors. Find the critical points. The sign can only change at 0 (zero). Test one point in each interval (sign chart). (-∞, 0): test x equals negative 1 → sign plus → excluded; (0, ∞): test x equals 1 → sign plus → excluded. Decide the endpoints. 0: excluded.

Steps, part 2. Write the solution set.

The answer. So the answer is No solution (∅). No real number satisfies the inequality.

Check. x equals negative 1: does not satisfy 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 x^2 < 0: Animated Inequalities Lesson, Step by Step