Answer:
x = [tex]\frac{1}{3}[/tex] & 3
Step-by-step explanation:
[tex]\frac{8x}{10x-2}[/tex] = [tex]\frac{5x+3}{7x}[/tex]
Cross multiply:
[tex]\frac{8x}{10x-2}[/tex] = [tex]\frac{5x+3}{7x}[/tex] ⇒ (8x)(7x) = (5x+3)(10x-2)
Simplify both sides:
(8x)(7x) = (5x+3)(10x-2) ⇒ 56x² = 50x²+20x-6
Set equation equal to 0:
56x² = 50x²+20x-6 ⇒ 0 = -6x²+20x-6
Factor the trinomial:
0 = -6x²+20x-6 = (-6x+2)(x-3)
Solve for X:
-6x+2 = 0
-6x = -2
x = [tex]\frac{1}{3}[/tex];
x-3 = 0
x = 3;
x = [tex]\frac{1}{3}[/tex], 3
