For what values of the following expressions are true: |a−5|=5−a

Whenever a-5<0 or a<5

Step-by-step explanation:

So if you have an absolute value, that turns into two equations. The one we care about is -(a-5)=5-a. After distributing the negative through the left side of the equation, you'll get that 5-a=5-a, which is an identity. But you can only say that abs(a-5)=5-a when a-5<0. To see a visual representation of this, graph both sides of the equation in desmos.

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

30005

yes ok