Question

uto and Hila attempted to solve the same inequality. Their work is shown below.

Yuto’s Work
Hila’s Work
Negative two-thirds x + 9 greater-than 7. Negative two-thirds x + 9 minus 9 greater-than 7 minus 9. Negative two-thirds x greater-than negative 2. (Negative three-halves) (Negative two-thirds x) less-than (Negative three-halves) (Negative StartFraction 2 over 1 EndFraction). x less-than 3.
Negative two-thirds x + 9 greater-than 7. Negative two-thirds x + 9 minus 9 greater-than 7 minus 9. Negative two-thirds x greater-than 16. (Negative three-halves) (Negative two-thirds x) less-than (Negative three-halves) (StartFraction 16 over 1 EndFraction). x less-than negative 24.

Which statement is true about the work shown above?
Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
Yuto is incorrect because he should not have reversed the inequality symbol.
Hila is correct because she isolated the variable correctly and reversed the inequality symbol.
Hila is incorrect because she should not have reversed the inequality symbol.

Answer 1

Yuto is correct because he isolated the variable properly and reversed the inequality when multiplying by a negative.

Work: -2/3 x + 9 > 7 → -2/3 x > -2 → multiply by -3/2 (negative) flips > to <: x < 3.

Hila is wrong (she made an arithmetic error: 7 − 9 = −2, not 16).