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.