Question

A set of kitchen appliances for a new home is $3,200. An installment loan requires a 10% down payment. The loan is 21% APR over 3 years. What is the total amount of carrying charges?

Answer 1

To solve the inequality '-5x ≥ 2x + 21', we isolate the variable x to find that x must be greater than or equal to -3.

Step-by-step explanation:

The question involves solving an inequality where the opposite of five times a number is at least 21 more than two times that same number. To translate this into a mathematical inequality, we let x represent the number. The 'opposite of five times a number' is -5x, and 'two times that same number' is 2x. The phrase 'at least 21 more than' translates to the inequality being greater than or equal to 21.

Therefore, the inequality is written as:

-5x ≥ 2x + 21

To solve the inequality, we need to isolate the variable x:

1. Add 5x to both sides to get 0 ≥ 7x + 21.
2. Subtract 21 from both sides to find 0 ≥ 7x, or equivalently 7x ≥ -21.
3. Divide both sides by 7 to get x ≥ -3.

The solution to the inequality indicates that x must be greater than or equal to -3.