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InequalitiesAlgebraHigh schoolabout 1:12

Solve |2x + 5| > 6: animated lesson

A narrated, step-by-step inequalities video lesson with captions. Final answer: x < -11/2 or x > 1/2; interval notation: (−∞, -11/2) ∪ (1/2, ∞).

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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 (0.5 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
$|2x + 5| > 6$
2. Step by step
1. $|2x + 5| > 6$
  Write the problem with the absolute value isolated
2. $2x + 5 < -6 \quad\text{or}\quad 2x + 5 > 6$
  Split into two ("or") inequalities
3. $2x + 5 = -6 \;\Rightarrow\; 2x = -6 - 5 = -11 \;\Rightarrow\; x = -\frac{11}{2} \\ 2x + 5 = 6 \;\Rightarrow\; 2x = 6 - 5 = 1 \;\Rightarrow\; x = \frac{1}{2}$
  Find the boundary points
4. $(-\infty,\ -\frac{11}{2}) \cup (\frac{1}{2},\ \infty)$
  Write the solution set in interval notation
3. The answer
$x < -\frac{11}{2} \quad\text{or}\quad x > \frac{1}{2} \qquad (-\infty,\ -\frac{11}{2}) \cup (\frac{1}{2},\ \infty)$
|2x + 5| > 6 → x < -11/2 or x > 1/2
4. Check
- Test point x = -5/2 (between the endpoints): |0| = 0, which is not > 6, so the middle region is excluded.

Transcript

The problem. Here is the problem: |2x plus 5| greater than 6. 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. Split into two ("or") inequalities. The inside must be at least c units away from zero, on either side. Find the boundary points. The solution lies outside the endpoints. Write the solution set in interval notation.

The answer. So the answer is x less than negative 11 over 2 or x greater than 1 over 2; interval notation: (−∞, negative 11 over 2) ∪ (1 over 2, ∞). 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).

Check. Test point x equals negative 5 over 2 (between the endpoints): |0| equals 0, which is not greater than 6, so the middle region is excluded.

About inequalities

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

Solve |2x + 5| > 6: Inequalities Step-by-Step Lesson