-2/5x-9<9/10
basically just solving for x but whatever that's called in an inequality
-2/5x - 9 < 9/10
multiply by 10 to get rid of those pesky fractions
-4x - 90 < 9
-4x < 81
x > 81/-4
or maybe you meant
-2/(5x-9) < 9/10
-20/(5x-9) < 9
Now you have two solutions, depending on whether 5x-9 > 0
If 5x-9 > 0, then -20 < 9(5x-9)
If 5x-9 < 0 then -20 > 9(5x-9)
-2x/5 - 9 < 9/10.
Multiply both sides by 10:
-4x - 90 < 9,
-4x < 9 + 90,
-4x < 99,
X > -99/4.
X > -24 3/4.
To solve the inequality -2/5x - 9 < 9/10, you need to isolate the variable x. Here's how you can do it step-by-step:
Step 1: Get rid of the constant term on the left side. In this case, you need to add 9 to both sides of the inequality:
-2/5x - 9 + 9 < 9/10 + 9
-2/5x < 9/10 + 90/10
-2/5x < 99/10
Step 2: Simplify the right side of the inequality:
-2/5x < 99/10
Step 3: Multiply both sides of the inequality by (-5/2). Remember that when you multiply or divide by a negative number, the inequality symbol flips:
(-5/2)(-2/5x) > (-5/2)(99/10)
x > -495/20
Step 4: Simplify the right side of the inequality:
x > -2475/100
x > -24.75
So the solution to the inequality is x > -24.75.