The equation 5x - 7 (x-1) = ax+b has exactly one solution.

a = - 2 and b = 7

Step-by-step explanation:

We need to solve for the value of "a" and "b".

We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.

We will use the distributive property shown below to expand the left side and simplify.

Distributive Property: a (b-c) = ab - ac

Now, simplifying left hand side:

5x - 7 (x - 1)

= 5x - 7 (x) - 7 (-1)

= 5x - 7x + 7

= - 2x + 7

The right hand side is "ax + b".

If we match left-hand side and right-hand side, we see that:

a = - 2

and

b = 7

THese are the only solution.