An automobile salesman receives a monthly bonus cheque if his commission income is at least $6,800.00 in a given month. There are 49 automobiles on the lot for sale and he receives a commission of $850.00 per sale. Which inequality shows the number of automobiles, x, the salesman must sell in order for him to receive a bonus cheque at the end of the month?

The salesman earns $850 per automobile he sells.

Since x represents the amount of automobiles the salesman sells, we can apply the commission as a coefficient to this variable. Therefore, the total commission that the salesman earns can be represented by $850x.

The bonus cheque is only received if the salesman's commission income is at least $6,800. 'at least' means that the salesman can still receive the cheque if his commission is exactly $6,800. The sign that we can use for this situation is the greater than or equal to sign, ≥.

The inequality that shows the commission income needed for the cheque is $850x ≥ $6,800. However, this question asks for the number of automobiles the salesman must sell to get the cheque.

Divide both sides by $850, as that represents his sales from one commission:

x ≥ 8

The inequality x ≥ 8 represents the amount of automobiles the salesman will need to sell to get the bonus cheque.