-2/5x-9<9/10
Make it clear whether you mean
(-2/5)x - 9 < 9/10
-2/(5x) - 9 < 9/10
-2/(5x-9) < 9/10
It makes a difference, and as you can see, online text formatting does not fully reflect what you thought you were saying...
both sides are fractions sir.
To solve the inequality, we need to isolate the variable, "x". Let's break down the steps:
Step 1: Multiply both sides of the inequality by the denominator of the fraction on the left side (5) and the denominator of the fraction on the right side (10). By doing this, we can eliminate the denominators and make our calculations more manageable.
(5) * (-2/5x - 9) < (10) * (9/10)
This simplifies to:
-2x - 45 < 9
Step 2: Next, let's get rid of the constant term (-45) on the left side of the inequality by adding 45 to both sides:
-2x - 45 + 45 < 9 + 45
This simplifies to:
-2x < 54
Step 3: To isolate "x", we can divide both sides of the inequality by the coefficient (-2). However, since we are dividing by a negative number, the inequality sign will flip.
(-2x) / (-2) > 54 / (-2)
This simplifies to:
x > -27
Therefore, the solution to the inequality -2/5x - 9 < 9/10 is x > -27.