2ax-15=3(x+5)+5(x-1)

Question

In the equation above, a is a constant. If no value of x satisfies the equation, what is the value of a?

Answer 1

To start, let's use algebra to solve this equation for x:

2ax-15=3(x+5)+5(x-1)

2ax - 15 = 3x + 15 + 5x - 5

2ax - 15 = 8x +10

(2a - 8)x = 25

x = 25/(2a-8)

The only way that this equation does not have a solution is if 2a - 8 = 0, as that would mean x = 25/0, and we can't divide by 0. If 2a - 8 = 0, then a = 4. And so the original equation, 2ax-15=3(x+5)+5(x-1) will not have a solution when a = 4.