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InequalitiesAlgebraHigh schoolabout 1:17

Solve 7x + 4 <= 6x - 9: animated lesson

A narrated, step-by-step inequalities video lesson with captions. Final answer: (-∞, -13].

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 (0.5 MB) · Captions (WebVTT)

Steps on screen

  1. 1. The problem
    Worked example
    7x+4≤6x−97x+4 \le 6x-9
  2. 2. Step by step
    1. x≤−13x \le -13
      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 (-\infty, -13]
      Write the solution set
  3. 3. The answer
    (−∞,−13](-\infty, -13]

    x ∈ (-∞, -13]

  4. 4. Check
    • x = -14: satisfies the inequality.
    • x = -12: does not satisfy the inequality.

Transcript

The problem. Here is the problem: 7x plus 4 less than equals 6x minus 9. Solve the inequality and give the answer in interval notation.

Step by step. Move everything to one side and isolate the variable. Collect terms: x plus 13 less than or equal to 0. Test one point in each interval (sign chart). (-∞, negative 13): test x equals negative 14 → sign minus → included; (negative 13, ∞): test x equals negative 12 → sign plus → excluded. Decide the endpoints. negative 13: included (the expression equals 0 and the sign allows equality). Write the solution set.

The answer. So the answer is (-∞, negative 13]. The inequality holds exactly for x in (-∞, negative 13]. 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 14: satisfies the inequality. x equals negative 12: does not satisfy the inequality.

About inequalities

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

More lessons like this

Solve 7x + 4 <= 6x - 9: Inequalities Step-by-Step Lesson