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. 500 − 30x ≥ 200 −500 −500 −30x ≥ −300 x ≥ 10 Review Jamie's work. What was her error?

Step-by-step explanation:

Given the inequality solved by H=Jamie expressed as:

500 − 30x ≥ 200

We need to calculate the range of x of the inequality to determine the number of weeks she can spend $30 as shown:

500 − 30x ≥ 200

Subtract 500 from both sides

500 − 30x - 500≥ 200 - 500

− 30x ≥ -300

Divide both sides by -30

− 30x/-30 ≥ -300/-30

x ≤ 10 (note that the inequality sign changes after dividing both sides by a negative sign)

Jamie's error was that she didn't change the sense of inequality after dividing both sides by -30 hence rendering her solution incorrect

Hence the number of weeks is less than or equal to 10.

3rd box is the answer

step-by-step explanation:

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions