Question

alx+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 of b?

Answer 1

Answer:

a=4, b=5/2

Step-by-step explanation:

Assuming the given equation is

$a(x + b) = 4x + 10$

We expand the left hand side to get:

$ax + ab = 4x + 10$

If this equation must have infinitely many solutions, then

$ax = 4x \\ \implies \: a = 4$

Also we must have

$ab = 10$

Put a=4 to get:

$4b = 10$

$b = \frac{10}{4} = \frac{5}{2}$