Yuto and Hila attempted to solve the same inequality. Their work is shown. Yuto’s Work Hila’s Work negative 2 thirds x plus 9 is greater than 7 negative 2 thirds x plus 9 is greater than 7 negative 2 thirds x plus 9 minus 9 is greater than 7 minus 9 negative 2 thirds x plus 9 plus 9 is greater than 7 plus 9 negative 2 thirds x is greater than negative 2 negative 2 thirds x is greater than 16 open paren negative 3 halves close paren times open paren negative 2 thirds x close paren is less than open paren negative 3 halves close paren times open paren negative 2 over 1 close paren open paren negative 3 halves close paren times open paren negative 2 thirds x close paren is less than open paren negative 3 halves close paren times open paren 16 over 1 close paren x is less than 3 x is less than negative 24 Which statement is true about the work shown above?
Answer
A
Hila is correct because she isolated the variable correctly and reversed the inequality symbol.
B
Hila is incorrect because she should not have reversed the inequality symbol.
C
Yuto is incorrect because he should not have reversed the inequality symbol.
D
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
Explanation
Subtract 9 from both sides of −⅔x + 9 > 7 to get −⅔x > −2. Multiplying both sides by −3/2 changes the direction of the inequality, giving x < 3. Yuto’s result is correct; Hila incorrectly added 9 instead of subtracting it.
AI-written and checked against the verified answer.