Question

What is the value of x?
A.5
B.2.5
C.7.5
D.10

Answer 1

`\text{We have proportion:}\\\\(x)/(x-2)=(x+5)/(x+1)\qquad\text{cross multiply}\\\\x(x+1)=(x-2)(x+5)\qquad\text{use distributive property and FOIL method}\\\\(x)(x)+(x)(1)=(x)(x)+(x)(5)+(-2)(x)+(-2)(5)\\\\x^2+x=x^2+5x-2x-10\qquad\text{subtract}\ x^2\ \text{from both sides}\\\\x=3x-10\qquad\text{subtract 3x from both sides}\\\\-2x=-10\qquad\text{divide both sides by (-2)}\\\\x=5\\\\Answer:\ \boxed{A.\ 5}`