Question

2 mod ( 3-x ) + 3 mod ( x - 1 ) = 4​

Answer 1

Answer:

           x = 1

Step-by-step explanation:

To solve 2 |3 - x| + 3 |x - 1| = 4, consider regions one at a time.

• Case x ≤ 1.  Then |x - 1| = -(x - 1) = 1 - x.  Also, x<3 so |3 - x| = 3 - x.  The equation then becomes 2(3-x) + 3(1-x) = 4  ⇒  5x = 5  ⇒  x = 1.
• Case 1 < x ≤ 3.  Then |x - 1| = x - 1 and |3 - x| = 3 - x.  So the equation becomes 2(3-x)+3(x-1) = 4  ⇒  x = 1, which does not satisfy 1 < x ≤ 3, so there is no solution in this region.
• Case 3 < x.  Then |x - 1| = x - 1 and |3 - x| = x - 3.  So the equation becomes 2(x-3)+3(x-1) = 4  ⇒  x = 13/5, which does not satisfy 3 < x, so there is no solution in this region.

Therefore there is only the one solution x = 1.

Hope this helps.