Skip to content
MathSolver Pro
  • Open the math solver
  • Ask the AI tutor
  • Find an AP course
  • Create a quiz
  • Open the calculator
  • Graphing Calculator
  • Browse all calculators
  • Read math guides
↑ ↓Enter to open · Esc to close
Solve a problem
Absolute value equationsAlgebraHigh schoolabout 1:00

Solve |-2x + 9| = 7: animated lesson

A narrated, step-by-step absolute value equations video lesson with captions. Final answer: x = 1 or x = 8; interval notation: {1, 8}.

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
    ∣−2x+9∣=7|-2x + 9| = 7
  2. 2. Steps, part 1
    1. ∣−2x+9∣=7|-2x + 9| = 7
      Write the problem with the absolute value isolated
    2. −2x+9=7or−2x+9=−7-2x + 9 = 7 \quad\text{or}\quad -2x + 9 = -7
      Split into two cases
    3. −2x+9=7  ⇒  −2x=7−9=−2  ⇒  x=1-2x + 9 = 7 \;\Rightarrow\; -2x = 7 - 9 = -2 \;\Rightarrow\; x = 1
      Solve the positive case
    4. −2x+9=−7  ⇒  −2x=−7−9=−16  ⇒  x=8-2x + 9 = -7 \;\Rightarrow\; -2x = -7 - 9 = -16 \;\Rightarrow\; x = 8
      Solve the negative case
  3. 3. Steps, part 2
    1. ∣−2⋅1+9∣=∣7∣=7∣−2⋅8+9∣=∣−7∣=7|-2\cdot 1 + 9| = |7| = 7 \\ |-2\cdot 8 + 9| = |-7| = 7
      Check each solution in the original equation
    2. {1, 8}\{1,\ 8\}
      Write the solution set in interval notation
  4. 4. The answer
    x=1orx=8{1, 8}x = 1 \quad\text{or}\quad x = 8 \qquad \{1,\ 8\}

    |-2x + 9| = 7 → x = 1 or x = 8

  5. 5. Check
    • Substituting 1 and 8 gives 7 on the left, matching the right-hand side.

Transcript

The problem. Here is the problem: |-2x plus 9| equals 7. Solve an absolute value equation by splitting it into the cases where the inside is positive or negative.

Steps, part 1. 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 cases. The inside is either c units above zero or c units below zero. Solve the positive case. Solve the negative case.

Steps, part 2. Check each solution in the original equation. Write the solution set in interval notation.

The answer. So the answer is x equals 1 or x equals 8; interval notation: 1, 8. An absolute value measures distance from zero, so |u| equals c means u is exactly c units from zero on either side.

Check. Substituting 1 and 8 gives 7 on the left, matching the right-hand side.

About absolute value equations

Solve equations with absolute values by splitting them into two cases.

More lessons like this

Solve |-2x + 9| = 7: Absolute value equations Lesson