I need help with this inequality, I'm not sure how to solve for 's'.
1 ⅓s - 3 < s + ⅔ - ⅓s
To solve for 's' in the given inequality:
1 ⅓s - 3 < s + ⅔ - ⅓s
First, let's simplify both sides of the inequality by combining like terms:
1 ⅓s - 3 < s + ⅔ - ⅓s
To simplify the left-hand side, we add the coefficients of 's':
(s + ⅓s) - 3 < s + ⅔ - ⅓s
(4/3)s - 3 < s + ⅔ - ⅓s
(4/3)s - 3 < s - (1/3)s + ⅔
To simplify the right-hand side, we combine the constants:
(4/3)s - 3 < (2/3)s + ⅔
Now, let's gather all the terms containing 's' on the left side of the inequality by subtracting (2/3)s from both sides:
(4/3)s - (2/3)s - 3 < (2/3)s - (2/3)s + ⅔
(2/3)s - 3 < ⅔
Next, we get rid of the denominators by multiplying both sides of the inequality by the LCD, which is 3:
3 * [(2/3)s - 3] < 3 * (⅔)
2s - 9 < 2
Now, we can isolate 's' by adding 9 to both sides of the inequality:
2s - 9 + 9 < 2 + 9
2s < 11
Finally, we solve for 's' by dividing both sides of the inequality by 2:
(2s)/2 < 11/2
s < 5.5
Therefore, the solution for 's' is s < 5.5.
The first thing I'd do is multiply by 3 to clear all the fractions:
4s - 9 < 3s + 2 - s
4s - 9 < 2s + 2
2s < 11
s < 11/2