1. Determine the possible range of values for x that satisfy the inequality 2x + 5 > 10.
We can solve this inequality by subtracting 5 from both sides: 2x + 5 - 5 > 10 - 5, which simplifies to 2x > 5. Next, we divide both sides by 2 to solve for x: 2x/2 > 5/2, which simplifies to x > 5/2. Therefore, the possible range of values for x that satisfy the inequality is x > 5/2 or x > 2.5.
2. At a movie theater, the cost of a ticket is $12.00. You have $40.00 in your wallet. What is the maximum number of tickets you can buy?
To determine the maximum number of tickets you can buy, we need to solve the inequality 12x ≤ 40, where x represents the number of tickets. Dividing both sides by 12 gives us x ≤ 40/12, which simplifies to x ≤ 3.33. Since you cannot buy a fraction of a ticket, the maximum number of tickets you can buy is 3.
3. Solve the inequality -3x + 7 ≥ -2x + 10.
To solve this inequality, we can start by subtracting -2x from both sides: -3x + 7 - (-2x) ≥ -2x + 10 - (-2x), which simplifies to -3x + 2x + 7 ≥ -2x + 2x + 10, further simplifying to -x + 7 ≥ 10. Next, subtract 7 from both sides: -x + 7 - 7 ≥ 10 - 7, which simplifies to -x ≥ 3. Finally, multiply both sides by -1 to solve for x and flip the inequality sign: -x(-1) ≤ 3(-1), which simplifies to x ≤ -3. The solution to the inequality is x ≤ -3.
4. A train is traveling at a speed of 60 miles per hour. The maximum speed limit on the highway is 70 miles per hour. What is the maximum speed the train can exceed the speed limit without receiving a ticket?
To determine the maximum speed the train can exceed the speed limit without receiving a ticket, we need to solve the inequality 60 + x ≤ 70, where x represents the maximum speed over the speed limit allowed. Subtracting 60 from both sides gives us x ≤ 70 - 60, which simplifies to x ≤ 10. Therefore, the train can exceed the speed limit by a maximum of 10 miles per hour without receiving a ticket.
Applications of inequalities quick check
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