How do solve (2x)/(x-2)<=3 algebraically?
2 Answers
Multiply both sides by
Distribute the 3
Move
Divide out negative one from both sides
*When dividing or multiplying by a negative, you have to switch the greater or less than sign.
Explanation:
"subtract 3 from both sides"
(2x)/(x-2)-3<=0
"combine the left side as a single fraction"
(2x)/(x-2)-(3(x-2))/(x-2)<=0
(6-x)/(x-2)<=0
"find the critical values of numerator/denominator"
6-x=0rArrx=6larrcolor(blue)"is a zero"
x-2=0rArrx=2
"these values divide the domain into 3 intervals"
(-oo,2)uu(2,6]uu[6,oo)
"select a value for x as a "color(red)"test point in each interval"
x=1to(6-1)/(1-2)=-5<0larrcolor(blue)"valid"
x=3to(6-3)/(3-2)=3>0larrcolor(blue)"not valid"
x=10to(6-10)/(10-2)=-1/2<0larrcolor(blue)"valid"
x in(-oo,2)uu[6,oo)
graph{(2x)/(x-2)-3 [-10, 10, -5, 5]}
