Question

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

Answer 1

x < -7 or x > 13

Explanation:

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

-x < -13 or -x > 7

x > 13 or x < -7

Answer: x < -7 or x > 13

Answer 2

x < -7 or x > 13

Explanation:

Solving Absolute Value

• 
  `|-x+3| > 10`
• We know that either -x + 3 > 10 or -x + 3 < -10

Possibility 1:

Step 1: Subtract 3 from both sides.

• 
  `-x + 3-3>10-3`
• 
  `-x > 7`

Step 2: Divide both sides by -1.

• 
  `(-x)/(-1) > (7)/(-1)`
• 
  `x < -7`

Possibility 2:

Step 1: Subtract 3 from both sides.

• 
  `-x + 3 - 3 < -10 - 3`
• 
  `-x < -13`

Step 2: Divide both sides by -1.

• 
  `(-x)/(-1) < (-13)/(-1)`
• 
  `x > 13`

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