at the beginning of the school year, jamie had $500 in her savings account. she wants to have at least $200…

at the beginning of the school year, jamie had $500 in her savings account. she wants to have at least $200 left in the account at the end of the school year. each week, she withdraws $30 for spending money. to determine how many weeks she can spend $30, jamie wrote and solved this inequality.\n\n$500 - 30x \\ge 200$\n$-500 \\quad -500$\n$-30x \\ge -300$\n$x \\ge 10$\n\nreview jamies work. what was her error?\n- jamie should have used the less than or equal to sign when writing the inequality.\n- jamie should have reversed the inequality when using the division property of inequality.\n- jamie should have added 500 to both sides.\n- jamie should have started by dividing by -30.

at the beginning of the school year, jamie had $500 in her savings account. she wants to have at least $200 left in the account at the end of the school year. each week, she withdraws $30 for spending money. to determine how many weeks she can spend $30, jamie wrote and solved this inequality.\n\n$500 - 30x \\ge 200$\n$-500 \\quad -500$\n$-30x \\ge -300$\n$x \\ge 10$\n\nreview jamies work. what was her error?\n- jamie should have used the less than or equal to sign when writing the inequality.\n- jamie should have reversed the inequality when using the division property of inequality.\n- jamie should have added 500 to both sides.\n- jamie should have started by dividing by -30.

Answer

Explanation:

Step1: Identify the initial inequality

Jamie correctly modeled the situation where the remaining balance must be at least $$200$. $$500 - 30x \geq 200$$

Step2: Subtract 500 from both sides

Jamie correctly subtracted $500$ from both sides of the inequality. $$-30x \geq -300$$

Step3: Divide by -30 and apply inequality rules

When dividing or multiplying an inequality by a negative number, the inequality sign must be reversed. Jamie failed to reverse the sign. $$x \leq \frac{-300}{-30}$$

Step4: Determine the correct final result

The correct solution shows that Jamie can spend money for at most $10$ weeks. $$x \leq 10$$

Answer:

Jamie should have reversed the inequality when using the division property of inequality.