Equivalent means they are equal.
14.1x+b = 4.7(3x-3.5)
Solve for b. First subtract 15.1x to both sides.
b = 4.7(3x-3.5) - 14.1x
You can simplify by distributing the 4.7 and combining like terms.
b = 14.1x - 16.45 - 14.1x
The positive and negative 14.1x cancel each other out.
b = -16.45