What is the value of b when the expression 14.1x+b is equivalent to 4.7 (3x-3.5)

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