221k views
2 votes
Tell whether the value is a solution of the inequality

-5q - 7/4 + 8q less than 5/8 ; q = 5/6

1 Answer

4 votes

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.

User Dinos
by
9.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.