Solve the inequality:
-2/5x - 9 < 9/10
do you mean
-2/5x - 9 < 9/10 ???
or
(-2/5)(x - 9) < 9/10
or
-2/(5x - 9 )< 9/10
or
-2/[5(x - 9)] < 9/10
or
what ?
Write an equation for:Twelve times h equals one hundred and twenty minus thirty-six.
I think that the level of problems presented indicates the intent is
-2/5 x - 9 < 9/10
-4x - 90 < 9
-4x < 99
x > -99/4
Alexia, that would be 12h = 120-36
To solve the inequality, we want to isolate the variable x. Here's how we can do that:
Step 1: Simplify both sides of the inequality.
-2/5x - 9 < 9/10
First, let's simplify -2/5x. To do this, we can multiply both sides of the equation by -5/2, which is the reciprocal of -2/5:
(-5/2) * (-2/5x - 9) < (-5/2) * (9/10)
x + 45/2 < -45/10
After multiplying, we get:
x + 45/2 < -45/10
Step 2: Simplify the constants on the right side of the inequality.
To simplify -45/10, we can multiply both the numerator and the denominator by -10 to make them integers:
x + 45/2 < -45/10
x + 45/2 < -(-450/100)
x + 45/2 < 450/100
After simplifying, we get:
x + 45/2 < 9/2
Step 3: Move the constant term to the other side of the inequality.
To do this, we need to subtract 45/2 from both sides:
x + 45/2 - 45/2 < 9/2 - 45/2
x < -36/2
After simplifying, we get:
x < -18
So, the solution to the inequality is x < -18.