After you clear the fraction, see if you can factor the left-hand side. Do both sides involve $(x - 3)$ somehow?

If two expressions involving $x$ are equal for every value of $x$, what does that tell you about the coefficients (the numbers multiplying each factor) on each side?

In one expression line, type f(x) = 5x - 15. In another line, type g(x) = (b*(x - 3))/2. Desmos will automatically create a slider for b.

Move the b slider and watch how the graph of g(x) moves. You want the graphs of f(x) and g(x) to lie exactly on top of each other for all x-values shown.

When the two graphs coincide everywhere, read the corresponding value of b from the slider. That value makes the equation true for all real numbers x.

The phrase “true for all real numbers $x$” means the two expressions are identical, not just equal for one or two special values of $x$. So we should simplify both sides so they look the same expression.

Multiply both sides of the equation by $2$ to get rid of the denominator:

Simplify the left side:

Notice that $10x - 30$ has a common factor of $10$:

So the equation becomes

Since the equation must hold for all $x$, the two expressions $10(x - 3)$ and $b(x - 3)$ must be the same. For any $x \ne 3$, we can divide both sides by $(x - 3)$ to get

So the value of $b$ is 10.