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InequalitiesAlgebraHigh schoolabout 1:13

Solve 9x + 5 >= -9x - 1: animated lesson

A narrated, step-by-step inequalities video lesson with captions. Final answer: [-1/3, ∞).

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. 1. The problem
    Worked example
    9x+5≥−9x−19x+5 \ge -9x-1
  2. 2. Step by step
    1. x≥−13x \ge -\frac{1}{3}
      Move everything to one side and isolate the variable
    2. Test one point in each interval (sign chart)
    3. Decide the endpoints
    4. x∈[−13,∞)x \in [-\frac{1}{3}, \infty)
      Write the solution set
  3. 3. The answer
    [−13,∞)[-\frac{1}{3}, \infty)

    x ∈ [-1/3, ∞)

  4. 4. Check
    • x = -2: does not satisfy the inequality.
    • x = 1: satisfies the inequality.

Transcript

The problem. Here is the problem: 9x plus 5 greater than equals negative 9x minus 1. Solve the inequality and give the answer in interval notation.

Step by step. Move everything to one side and isolate the variable. Collect terms: 18x plus 6 greater than or equal to 0. Test one point in each interval (sign chart). (-∞, negative 1 over 3): test x equals negative 2 → sign minus → excluded; (negative 1 over 3, ∞): test x equals 1 → sign plus → included. Decide the endpoints. negative 1 over 3: included (the expression equals 0 and the sign allows equality). Write the solution set.

The answer. So the answer is [-1 over 3, ∞). The inequality holds exactly for x in [-1 over 3, ∞). 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 2: does not satisfy the inequality. x equals 1: satisfies the inequality.

About inequalities

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

More lessons like this

Solve 9x + 5 >= -9x - 1: Inequalities Step-by-Step Lesson