inequality solving & word problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, or equal to the other. Examples include <, >, ≤, and ≥.

Front

How do you solve the inequality 6(n + 2) < -72?

Back

First, distribute: 6n + 12 < -72. Then, subtract 12 from both sides: 6n < -84. Finally, divide by 6: n < -14.

Front

What does the inequality 15h ≥ 105 represent in a word problem?

Back

It represents the minimum number of hours (h) Johnny needs to work to earn at least $105 for a new bike, given he earns $15 per hour.

Front

How do you set up an inequality for the cost of DVD rentals at Papaya compared to Hutto?

Back

Let d be the number of DVDs rented. The inequality is 10 + 5d < 60 + 2d, meaning Papaya's total cost is less than Hutto's.

Front

What is the maximum number of miles Sue and Cathy can travel in a cab if the fare is $3 per mile plus a $2 fixed charge?

Back

The inequality is 3x + 2 ≤ 20, where x is the number of miles. This shows they can spend up to $20.

Front

What does the inequality k ≤ 62 represent?

Back

It represents the height restriction for kids allowed to play on the playground, meaning they must be no taller than 62 inches.

Front

What is the first step in solving the inequality 10 + 5d < 60 + 2d?

Back

The first step is to isolate the variable d by subtracting 2d from both sides: 10 + 3d < 60.

Front

How do you interpret the solution n < -14 in a real-world context?

Back

It means that the value of n must be less than -14, which could represent a situation where a certain quantity or measurement is below a specific threshold.

Front

What is the significance of the fixed charge in the cab fare problem?

Back

The fixed charge ($2) is a one-time fee that must be paid regardless of the distance traveled, affecting the total cost.

Front

How can you check if your solution to an inequality is correct?

Back

You can check by substituting a value from the solution set back into the original inequality to see if it holds true.