solve (x+2)/x>=0.2 with steps

x/x + 2/x ≥ .2

1 + 2/x ≥ .2

2/x ≥ -.8

2 ≥ -.8 x

-5/2 ≤ x

(x+2)/x >= 1/5

If x>0,
x+2 >= x/5
4x/5 >= -2
x >= -5/2
So, x > 0

If x<0,
x+2 <= x/5
4x/5 <= -2
x <= -5/2
So, x <= -5/2

So, in interval notation, x is in
(-∞,-5/2]U(0,∞)

I found the same answer but answer is

x<-5/2

see on wolfram alpha

thanks steve

To solve the inequality (x + 2)/x ≥ 0.2, we can follow these steps:

Step 1: Multiply both sides of the inequality by x to eliminate the fraction:

(x + 2)/x * x ≥ 0.2 * x
x + 2 ≥ 0.2x

Step 2: Distribute 0.2 to both terms on the right side:

x + 2 ≥ 0.2x
x + 2 ≥ 0.2x
x + 2 ≥ 0.2x
x + 2 ≥ 0.2x
x + 2 ≥ 0.2x
x + 2 - 0.2x ≥ 0
x + 2 - 0.2x ≥ 0
x + 2 - 0.2x ≥ 0
0.8x + 2 ≥ 0

Step 3: Subtract 2 from both sides:

0.8x + 2 - 2 ≥ 0 - 2
0.8x ≥ -2

Step 4: Divide both sides by 0.8 to isolate x:

(0.8x)/0.8 ≥ -2/0.8
x ≥ -2.5

Therefore, the solution to the inequality (x + 2)/x ≥ 0.2 is x ≥ -2.5.