Answer:
x = 11
Step-by-step explanation:
According to proportionality theorem, the transversal is divided proportionally as it cuts across parallel lines l, m, and n.
Therefore:
[tex] \frac{12.8}{x + 5} = \frac{x - 3}{10} [/tex]
Cross multiply
[tex] (12.8)(10) = (x + 5)(x - 3) [/tex]
[tex] 128 = x^2 - 3x + 5x - 15 [/tex]
[tex] 128 = x^2 + 2x - 15 [/tex]
[tex] 0 = x^2 + 2x - 15 - 128 [/tex]
[tex] 0 = x^2 + 2x - 143 [/tex]
Factorise:
[tex] 0 = x^2 - 11x + 13x - 143 [/tex]
[tex] 0 = x(x - 11) +13(x - 11) [/tex]
[tex] 0 = (x - 11)(x + 13) [/tex]
x = 11 or x = -13
We'd take the positive value.
Therefore, the value of x is 11.
