Question

Soro bought a $50. 00 bus card at the beginning of the week. Each bus ride costs $2. 50. He needs to have at least $20. 00 on his card at the end of this month. To determine how many bus rides he can take between now and the end of this month, Soro wrote and solved the following inequality: 50 minus 2. 5 x greater-than-or-equal-to 20. Negative 2. 5 x greater-than-or-equal-to negative 30. X greater-than-or-equal-to 12. What error, if any, did Soro make when writing or solving this inequality? Soro’s original inequality should have been 50 minus 2. 5 x less-than-or-equal-to 20. Soro should have added 2. 5 to each side for his first step. Soro should have reversed the inequality symbol when using the division property of inequality. Soro’s work shows no errors.

Answer 1

The error Soro makes while solving inequality is that "Soro should have reversed the inequality symbol when using the division property of inequality".

What are inequalities?

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The inequality is given as 50-2.5x≥20, now solving the inequality,

$50-2.5x \geq 20\\\\\text{Subtract -50 from both the sides}\\\\50-2.5x -50\geq 20-50\\\\-2.5\geq -30$

Divide both sides of the inequality by -2.5x, therefore, reverse the inequality symbol when using the division property of inequality.

$\dfrac{-2.5x}{-2.5} \leq \dfrac{-30}{-2.5}\\\\x \leq 12$

Hence, the error Soro makes when writing or solving inequality 50-2.5x≥20, is that "Soro should have reversed the inequality symbol when using the division property of inequality".

Learn more about Inequality:

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