The directors of a dance show expect many students to participate but don’t yet know how many students will come. The directors need 7 students to work on the technical crew. The rest of the students work on dance routines in groups of 9. For the show to work, they need at least 6 full groups working on dance routines.

Inequality is known to be a statement that shows the step or order association either it is greater than, equal to, less than, etc., that exist between two or more numbers in an expression.

Note that 7 students are in the technical crew. Denote the number of students in a group as = x

We take the other students in dance routines in groups of 9 as 9x.

Therefore, we say that the total number of students = 9x + 7

Since 6 full groups are working on dance routines, we then multiply by the student dance groups = 9 x 6 = 54

Therefore, we can state that our inequality as:

9x + 7 ≥ 54

Then you collect like terms:

9x ≥ 54 - 7

9x ≥ 47

x ≥ 47/9

x ≥ 6

So therefore, I will write to directors that the number of students they need in each group should be at least 6 students.

See full question below

1. Write and solve an inequality to represent this situation.

2. Write a sentence to the directors about the number of students they need.

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