solve the inequality
8/x+3/4/<2 used / / for brakets around x+3/4
possible answers
x<-1 or x>-1/2
-5/32<x<5/32
-1<x<-1/2
x<-5/32 or x>5/32
not looking for just the answer but help on how to do it
8(x + 3/4) < 2
8x + 6 < 2
8x < -4
x < -1/2
Ahh. by brackets you mean || for absolute value?
8|x + 3/4| < 2
if x+3/4 >= 0, then
x < -1/2 as above
if x+3/4 < 0, then
-8(x + 3/4) < 2
-8x - 6 < 2
-8 < 8x
x > -1
-1 < x < -1/2
To solve the inequality 8/(x+3/4) < 2, you can follow these steps:
1. Multiply both sides of the inequality by (x + 3/4) to eliminate the fraction:
(x + 3/4) * 8 / (x + 3/4) < 2 * (x + 3/4)
8 < 2(x + 3/4)
2. Simplify both sides of the inequality:
8 < 2x + 3/2
3. Subtract 2x from both sides of the inequality:
8 - 2x < 3/2
4. Subtract 8 from both sides of the inequality:
-2x < 3/2 - 8
5. Simplify the right side of the inequality:
-2x < -13/2
6. Divide both sides of the inequality by -2. Note that when dividing by a negative number, the inequality symbol reverses direction:
(-2x) / -2 > (-13/2) / -2
x > 13/4
Now you have the solution x > 13/4. However, this is not one of the possible answers you provided. Let's check the options given:
a. x < -1 or x > -1/2: This option does not match the solution found.
b. -5/32 < x < 5/32: This option does not match the solution found.
c. -1 < x < -1/2: This option does not match the solution found.
d. x < -5/32 or x > 5/32: This option does not match the solution found.
Therefore, none of the given options match the solution. The correct solution to the inequality 8/(x+3/4) < 2 is x > 13/4.
To solve the inequality, 8/x + 3/4 < 2, we'll follow these steps:
Step 1: Get rid of any fractions by multiplying both sides of the inequality by the least common denominator (LCD), which is 4x in this case. This eliminates the fractions and gives us a simpler form of the inequality.
4x(8/x + 3/4) < 4x(2)
Simplifying this expression, we have:
32 + 3x < 8x
Step 2: Rearrange the inequality so that all the terms involving x are on one side of the inequality and the constant term is on the other side.
Subtracting 3x from both sides:
32 < 8x - 3x
Simplifying, we get:
32 < 5x
Step 3: Divide both sides of the inequality by 5 to solve for x. Remember to reverse the inequality sign if you divide by a negative number.
Dividing both sides by 5:
6.4 < x
Simplifying, we have:
x > 6.4
So, the solution to the inequality is x > 6.4.
However, none of the possible answers provided match the correct solution. It seems that there is an error in the given possible answers.