What is the value for b?

Question

a(x+b)=4x+10

In the equation above, a and b are constants. If the equation has infinitely many solutions for X, what is the value for b?

Answer 1

a(x+b)=4x+10

ax + ab = 4x + 10 [use distributive principle]

Now for the two sides of that equation to be true for any value of x ("infinitely many solutions for x"),

a = 4

and

ab = 10

That is, scalars must be precisely the same and coefficients of x must be precisely the same.

Since a=4,

4b = 10

b = 10/4

b = 5/2

Check:

Does 4(x + 5/2) = 4x + 10 ?

4x + 10 = 4x + 10 ? yes, true for all values of x