Question

as a salesperson, cecil is paid $50 per week, plus $12 per sale. this week cecil wants to make at least $146. solve the inequality for the number of sales cecil needs to make this week, in dollars. use x to represent the number of sales and do not include any $ symbols in the inequality. show your work here hint: to add inequalities (<, >, ≤, ≥), type \less\ or \greater\

Explanation:

Step1: Define the total pay formula

Cecil's total pay is the base pay plus the pay from sales. The base pay is $50, and for \( x \) sales, the pay from sales is \( 12x \). So total pay \( P = 50 + 12x \).

Step2: Set up the inequality

He wants to make at least $146, so \( 50 + 12x \geq 146 \).

Step3: Solve the inequality

Subtract 50 from both sides: \( 12x \geq 146 - 50 \) → \( 12x \geq 96 \).
Divide both sides by 12: \( x \geq \frac{96}{12} \) → \( x \geq 8 \).

Answer:

The inequality is \( 50 + 12x \geq 146 \) (and the solution is \( x \geq 8 \)).