What is the length of the interval of solutions to the inequality 1 ( is less than or equal to) 3-4x (is less than or equal to) 9?
I presume that I just plug in numbers for x? The problem is, that all the positive numbers I've tried have made them way less than one, when its supposed to be greater than or equal to. Are negative numbers the answer?
Thanks!
3 - 4x = 9
-4x = 6
x = -6/4 = -1.5 = highest value for x in interval of solutions.
With this, you should be able to do a similar process to find the lowest value to define "length of the interval of solutions".
I hope this helps. Thanks for asking.
To find the length of the interval of solutions to the inequality 1 ≤ 3-4x ≤ 9, you first need to solve the inequality for x. Then, you can determine the range of values for x that satisfy the inequality.
To start, let's solve the inequality step by step:
1 ≤ 3 - 4x ≤ 9
First, let's subtract 3 from all parts of the inequality:
1 - 3 ≤ 3 - 4x - 3 ≤ 9 - 3
-2 ≤ -4x ≤ 6
Next, divide all parts of the inequality by -4, remembering that dividing by a negative number changes the direction of the inequality:
(-2) ÷ -4 ≥ (-4x) ÷ -4 ≥ 6 ÷ -4
0.5 ≥ x ≥ -1.5
So, the solution for x is -1.5 ≤ x ≤ 0.5.
The length of the interval of solutions is found by subtracting the lower limit from the upper limit:
0.5 - (-1.5) = 2
Therefore, the length of the interval of solutions to the inequality is 2 units.
Negative numbers, in this case, are part of the solution. It's important to consider all possible values that satisfy the inequality when solving inequalities.