patricko19
Answered

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Solve this inequality algebracially. |3-x|>10

Sagot :

mathstudent55

Answer:

x < -7 or x > 13

Step-by-step explanation:

3 - x < -10 or 3 - x > 10

-x < -13      or    -x > 7

x > 13         or    x < -7

Answer: x < -7 or x > 13

renknee

Answer:

x < -7 or x > 13

Step-by-step explanation:

Solving Absolute Value

  • [tex]|-x+3| > 10[/tex]
  • We know that either -x + 3 > 10 or -x + 3 < -10

Possibility 1:

Step 1: Subtract 3 from both sides.

  • [tex]-x + 3-3>10-3[/tex]
  • [tex]-x > 7[/tex]

Step 2: Divide both sides by -1.

  • [tex]\frac{-x}{-1} > \frac{7}{-1}[/tex]
  • [tex]x < -7[/tex]

Possibility 2:

Step 1: Subtract 3 from both sides.

  • [tex]-x + 3 - 3 < -10 - 3[/tex]
  • [tex]-x < -13[/tex]

Step 2: Divide both sides by -1.

  • [tex]\frac{-x}{-1} < \frac{-13}{-1}[/tex]
  • [tex]x > 13[/tex]

Therefore, the answer is x < -7 or x > 13.

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