Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols such as <, >, ≤, or ≥.

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than' and indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than' and indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What is the difference between an open dot and a closed dot on a number line when graphing inequalities?

Back

An open dot indicates that the number is not included in the solution (used for < or >), while a closed dot indicates that the number is included in the solution (used for ≤ or ≥).

Front

How do you solve the inequality x + 5 > 7?

Back

To solve the inequality, subtract 5 from both sides: x > 2.

Front

What is the inequality that represents the cost of a taxi ride if the base fare is $1.75 and each additional mile costs $0.75, given a budget of $20?

Back

The inequality is 0.75m + 1.75 ≤ 20, where m is the number of additional miles.

Front

If a parking garage charges $4.50 per hour and you have $18, how do you express the maximum number of hours you can park?

Back

The inequality is x ≤ 4, where x is the number of hours.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left side can be less than or equal to the value on the right side.

Front

What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' means 'greater than or equal to' and indicates that the value on the left side can be greater than or equal to the value on the right side.

Front

How do you graph the inequality x < 3 on a number line?

Back

You place an open dot at 3 and shade to the left, indicating all values less than 3.