Question

|3x-2| ≥|x+4|
Please someone help me quick. Pls show working. You will eat brainliest and a thank for helping

Answer 1

Answer:

         x ≤ -1/2  or  x ≥ 3

Step-by-step explanation:

    |3x - 2|  ≥  |x + 4|

⇔  (3x - 2)²  ≥  (x + 4)²

⇔  9x² - 12x + 4  ≥  x² + 8x + 16

⇔  8x² - 20x - 12  ≥  0

⇔  2x² - 5x - 3  ≥  0

⇔  (2x + 1)(x - 3)  ≥  0

⇔  x ≤ -1/2  (so both factors are negative)  or  x ≥ 3 (so both factors are positive)