Unit 3, Lesson 16
Interpreting Inequalities
Accelerated 7
Practice
Problem 1
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.
Problem 2
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.
- Explain what \(x\) represents in the inequality.
- Solve the inequality.
- Explain what the solution means in the situation.
Problem 3
You know \(x\) is a number less than 4. Select all the inequalities that must be true.
\(x<2\)
\(x+6<10\)
\(5x<20\)
\(x-2>2\)
\(x<8\)
Problem 4
Match each sentence with the inequality that could represent the situation.
Han got $2 from Clare, but still has less than $20.
Mai spent $2 and has less than $20.
If Tyler had twice the amount of money he has, he would have less than $20.
If Priya had half the money she has, she would have less than $20.
\(x-2<20\)
\(2x<20\)
\(x+2<20\)
Problem 5
Find \(x\), \(y\), and \(z\).