Solving Inequalities

Front

What is the purpose of graphing solution sets to inequalities?

Back

To visually represent the range of values that satisfy the inequality.

Front

What does the inequality symbol '<' indicate about a value?

Back

It indicates that the solution is less than the specified value.

Front

How do you solve the inequality \( \frac{d}{2} - 1 \ge 3 \)?

Back

Add 1 to both sides to get \( \frac{d}{2} \ge 4 \), then multiply both sides by 2 to find \( d \ge 8 \).

Front

What does the inequality symbol '\ge' signify?

Back

It signifies that the solution is greater than or equal to the specified value.

Front

How can you determine which inequality matches a number line graph?

Back

By analyzing the endpoints and whether they are open or closed circles, and the direction of the shading.

Front

What is the difference between '<' and '\le'?

Back

'<' means less than, while '\le' means less than or equal to.

Front

What does the inequality symbol '>' represent?

Back

It represents that the solution is greater than the specified value.

Front

What is the solution set of the inequality \( x < 5 \)?

Back

All real numbers less than 5.

Front

How do you express the solution to the inequality \( x \ge 0 \) on a number line?

Back

Draw a closed circle at 0 and shade to the right.

Front

What is the significance of an open circle on a number line?

Back

It indicates that the endpoint is not included in the solution set.