x all over 2x+4 >= 1?

Question

Solve the inequality and give solution in interval notation
x/(2x+4)>= 1

Answer 1

x/(2x+4) - 1 >= 0

(x-2x-4)/(2x+4) >= 0

(x+4)/(2x+4) =< 0

since x =/= -2 (or else the denominator = 0 ) , multiply both side by(2x+4)^2

(x+4)(2x+4) =< 0 (with x =/= -2)

so considering the U shape quadratic graph those below the x-axis is -4 =< x < -2

or in interval form [-4,-2)

* i saw many answer just cross multiply the 2x+4 which is common mistake of many student . Recall that if u cross multiply a negative number , the inequality sign WILL change . So you cant be sure that the sign wont change if you just simply cross multiply . The easiest way to check whether Im talking the right thing is , just pick x = -10 and plug in the equation .

Answer 2

x/(2x+4)>= 1

x >= 2x + 4
-x >= 4
x <= -4

Multiplication or division by a negative number reverses the sense of the inequality.

Answer 3

x/(2x+4) >=1
restriction:
2x+4 must not equal 0
2x must not equal -4 /:2
x must not equal -2 (can be greater or less, but not equal)

x/(2x+4) >=1 /*(2x+4)
x >= 2x+4
x - 2x >= 4
-x >= 4 /*(-1) (inequality also changes its orientation: > turns into < )
x <= -4

x is the element of (infinity,-4] (includes all numbers less than -4, and -4 itself)

Answer 4

x / (2x + 4) >= 1

x >= 2x + 4

-x >= 4

x <= -4

Answer 5

i think it is x>=1