Answer:
x = { 4, 7 }
Step-by-step explanation:
given the equation
[tex]\frac{2}{(x-5)}[/tex] = [tex]\frac{x}{(3x-14)}[/tex] ( cross multiply )
x(x - 5) = 2(3x - 14) ← distribute parenthesis on both sides )
x² - 5x = 6x - 28 ( subtract 6x from both sides )
x² - 11x = - 28 ( add 28 to both sides )
x² - 11x + 28 = 0 ← in standard form
(x - 4)(x - 7) = 0 ← in factored form
equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x - 7 = 0 ⇒ x = 7
The solution is x = { 4, 7 }
