5 - sqrt of 20x + 4 >= -3
5- 20x + 4 >= -3
5-4 - 20x >= -3
1 - 20x >= -3-1
-20x >= -4
x<= -15
Possible answers are
x<=3
-1/5 <= x<= 3
x >= -1/5
x >= 0
I think it is -1/5<=x<=3
because both solutions work
I hate to say this, but each of your lines from
5- 20x + 4 >= -3
5-4 - 20x >= -3
1 - 20x >= -3-1
-20x >= -4
x<= -15
contains an error based on its previous line
First of all , if the question is
5 - √(20x + 4) >= -3 , then
√(20x+4) ≤ 8
consider the equation
√(20x+4) = 8
square both sides
20x+4 = 64
x = 3
so we have the region > 3 and the region < 3
A quick mental consideration in √(20x+4) ≤ 8 will show that only numbers ≤ 3 could work.
finally the inside of the square root cannot be negative,
that is,
20x + 4 ≥0
x ≥ -4/20
x ≥ -1/15
so x has to be between -1/5 and 3 , or
-1/5 ≤ x ≤ 3
Thank you
To solve the inequality 5 - sqrt(20x + 4) >= -3, let's go step by step.
Step 1: Isolate the square root expression on one side by subtracting -3 from both sides:
5 - sqrt(20x + 4) >= -3 - (-3)
5 - sqrt(20x + 4) >= 0
Step 2: Move the constant term (5) to the other side:
- sqrt(20x + 4) >= -5
Step 3: Square both sides of the inequality to eliminate the square root:
((- sqrt(20x + 4))^2) >= (-5)^2
20x + 4 >= 25
Step 4: Subtract 4 from both sides:
20x + 4 - 4 >= 25 - 4
20x >= 21
Step 5: Divide both sides by 20 to solve for x:
20x/20 >= 21/20
x >= 21/20
The solution to the inequality is x >= 21/20. However, when checking the possible answers you provided, it seems that there is an error in your work.
The correct solution is x >= 21/20, not x >= -1/5 or x >= 0. Therefore, the correct answer is:
x >= 21/20