How Do You Solve a Word Problem Using an Inequality Where You're Multiplying Negative Fractions?

Summary

'n' is a variable representing the 'number of wrong answers' the team gave
A wrong answer, 'n', gives the team -2/3 of a point
'(-2/3)n' represents the team's NEGATIVE score
The team's score is '≤ -8' because they could have gone below '-8' but may have given correct answers to bring their score back up to '-8'
Multiplying by '-3/2', the reciprocal of '-2/3', will let us solve for 'n'
The inequality sign is reversed because we multiplied by a negative number, '-3/2'

Notes

1. 'n' is a variable representing the 'number of wrong answers' the team gave
1. 'n' is a variable representing the 'number of wrong answers' the team gave
1. A wrong answer is represented by 'n', our unknown variable
1. A wrong answer is represented by 'n', our unknown variable
1. 'n' is a variable representing the 'number of wrong answers' the team gave
1. 'n' is a variable representing the 'number of wrong answers' the team gave
1. A correct answer would make their score increase
1. A correct answer would make their score increase
2. Correct answers could have brought their score up to '-8', so their score could have been below '-8' at some point
1. A correct answer would make their score increase
2. Correct answers could have brought their score up to '-8', so their score could have been below '-8' at some point
1. A correct answer would make their score increase
2. Correct answers could have brought their score up to '-8', so their score could have been below '-8' at some point
1. 'n' is a variable representing the 'number of wrong answers' the team gave
1. '-3/2' is the reciprocal of '-2/3'
1. 'n' is a variable representing the 'number of wrong answers' the team gave
2. '-3/2' cancels out the '-2/3', leaving us with 'n' on the left
3. -8 • (-3/2) = 12
1. '-3/2', the reciprocal of '-2/3', is the negative number we multiplied by
1. Multiplying by a negative number when dealing with an inequality means we have to reverse the inequality symbol
2. '-3/2', the reciprocal of '-2/3', is the negative number we multiplied by
1. 'n' is a variable representing the 'number of wrong answers' the team gave
2. -8 • (-3/2) = 12
3. Notice the inequality symbol has been reversed!
1. 'n' is a variable representing the 'number of wrong answers' the team gave
2. -8 • (-3/2) = 12
3. 'AT LEAST' translates to a '≥' symbol

At a particular trivia night a wrong answer results in scoring negative two-thirds of a point. If, at the end of a game, a team's total score is negative 8, how many answers could they have gotten wrong?

Summary

Notes