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.
