3/4(5/x-1/2)-5/3<1/3
3/20x-8-15<1/3
Check this for me where didi I go wrong
It is difficult to tell what the problem is, your use of ( ) is not clear.
expand and at the same time take the -5/3 to the other side
15/(4x) - 3/8 < 2
15/(4x) < 18/8
multiply by 8x
20 < 18x
x > 20/18
x > 10/9
To check where you might have gone wrong, let's go through your steps one by one.
Original equation: 3/4(5/x - 1/2) - 5/3 < 1/3
Step 1: Distribute 3/4 to (5/x - 1/2):
3/4 * 5/x - 3/4 * 1/2 - 5/3 < 1/3
Step 2: Simplify the expression:
15/4x - 3/8 - 5/3 < 1/3
Step 3: Find a common denominator for 4, 8, and 3, which is 24:
(15/4x) * (6/6) - (3/8) * (3/3) - (5/3) * (8/8) < 1/3
Step 4: Simplify the expression:
90/24x - 9/24 - 40/24 < 8/24
Step 5: Combine the fractions on the left side:
(90 - 9 - 40)/24x < 8/24
Step 6: Simplify further:
41/24x < 8/24
Now let's stop here and see if we can find where you made a mistake.
It seems like the mistake occurred in Step 2, where you subtracted 15 from both sides of the equation instead of subtracting it from 4x. Let's correct that step and continue from there:
Step 2 (Corrected): 15/4x - 3/8 - 5/3 < 1/3
Step 2 (Corrected): 15/4x - 3/8 - 40/24 < 8/24
Now, let's simplify the expression further:
Step 2 (Corrected): 15/4x - 9/24 - 40/24 < 8/24
Step 2 (Corrected): 15/4x - 49/24 < 8/24
Step 2 (Corrected): 15/4x < 57/24
Step 2 (Corrected): 15/4x < 19/8
Step 2 (Corrected): (15 * 8) / (4x) < 19/8
Step 2 (Corrected): 120 / (4x) < 19/8
Step 2 (Corrected): 30/x < 19/8
Now, you can proceed to solve the inequality by cross multiplying and finding the common denominator to continue simplifying the expression until you find the correct solution range.