How do you solve for inequalities like this?
1< 4-x < 1.59
split it
1<4-x
and
4-x<1.59
thanks.
1< 4-x < 1.59 subtract 4 from each part
-3 < -x < -2.41 now multiply each part by -1
3 > x > 2.41 or 2.41 < x < 3
To solve for inequalities like the one you provided (1 < 4-x < 1.59), you need to isolate the variable, in this case, x. Here's how you can do it step by step:
Step 1: Start by subtracting 4 from all three parts of the inequality:
1 - 4 < 4 - x - 4 < 1.59 - 4
-3 < -x < -2.41
Step 2: Divide all three parts of the inequality by -1. It's important to remember that when you divide by a negative number, the inequality symbol flips:
-3 / -1 > x > -2.41 / -1
3 > x > 2.41
So, the solution to the given inequality is 2.41 < x < 3.
By subtracting and dividing the equation, we were able to isolate the variable x and determine the range of values that satisfy the inequality.