Consider the equation 6x+15=-3 (ax-b), where a and b are real numbers. Which values for a and b will result in the equation having an infinite number of solutions?

A=-2 and b=5.

To have an infinite number of solutions, the two sides must be identical.

6x+15=-3 (ax-b)

Using the distributive property,

6x+15=-3*ax--3*b

6x+15=-3ax+3b

This means - 3ax=6x and 3b=15;

-3ax=6x

Divide both sides by - 3:

-3ax/-3 = 6x/-3

ax=-2x

Divide both sides by x:

ax/x=-2x/x

a=-2

3b=15

Divide both sides by 3:

3b/3=15/3

b=5