Answer:
the value q = 5/6 is not a solution to the inequality -5q - 7/4 + 8q < 5/8.
Explanation:
To determine whether the value q = 5/6 is a solution of the inequality -5q - 7/4 + 8q < 5/8, we can substitute the value of q into the inequality and simplify it.
Substituting q = 5/6 into the inequality:
-5(5/6) - 7/4 + 8(5/6) < 5/8
Simplifying the expression:
-25/6 - 7/4 + 40/6 < 5/8
To compare the fractions, we need to find a common denominator:
The common denominator for 6, 4, and 8 is 24. Multiplying each fraction by the appropriate factor to get the common denominator:
-100/24 - 42/24 + 160/24 < 15/24
Combining the fractions:
-100 - 42 + 160 < 15 (since the denominators are the same, we can compare the numerators)
-142 + 160 < 15
Simplifying further:
18 < 15
The inequality states that the left side must be less than the right side. However, in this case, 18 is not less than 15. Therefore, the value q = 5/6 is not a solution to the inequality -5q - 7/4 + 8q < 5/8.