Priya looks at the inequality \(12-x>5\) and says “I subtract a number from 12 and want a result that is bigger than 5. That means that the solutions should be values of \(x\) that are smaller than something.”

Do you agree with Priya? Explain your reasoning and include solutions to the inequality in your explanation.

Each day, a store opens with 175 shirts out on display. On average, 6 shirts are sold per hour. The store manager likes to keep at least 150 shirts on display at all times. If there are fewer than 150 on display, more shirts are brought out from the storeroom. The manager writes the inequality \(\text-6x+175 \geq 150\) to describe the situation.

1. Explain what \(x\) represents in the inequality.
2. Solve the inequality.
3. Explain what the solution means in the situation.

You know \(x\) is a number less than 4. Select all the inequalities that must be true.

Here is an unbalanced hanger diagram.

1. If you know each circle weighs 6 grams, what do you know about the weight of each triangle? Explain your reasoning.
2. If you know each triangle weighs 3 grams, what do you know about the weight of each circle? Explain your reasoning.

Match each sentence with the inequality that could represent the situation.

At a skateboard shop:

1. The price tag on a shirt says \$12.58. Sales tax is 7.5% of the price. How much will the shirt cost including tax?
2. The shop buys a helmet for \$19.00 and sells it for \$31.50. What percentage was the markup?
3. The shop pays workers \$14.25 per hour plus 5.5% commission. If someone works 18 hours and sells \$250 worth of merchandise, what is the total earning on their paycheck for this pay period? Explain or show your reasoning.