Graphing Inequalities

How do you solve the inequality @@x + 3 < 10@@?

• @@x < 7@@

• @@x > 7@@

• @@x = 7@@

• @@x + 3 = 10@@

What is an inequality?

• A mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

• A type of equation that has no solution.

• A statement that asserts the equality of two expressions.

• A graphical representation of a function.

How do you graph the inequality @@x > 12@@?

• Draw a number line, place an open circle on 12, and shade to the left to show all numbers less than 12.

• Draw a number line, place a closed circle on 12, and shade to the right to show all numbers greater than or equal to 12.

• Draw a number line, place an open circle on 12, and shade to the right to show all numbers greater than 12.

• Draw a number line, place a closed circle on 12, and shade to the left to show all numbers less than 12.

What is the difference between an open circle and a closed circle on a graph?

• An open circle indicates that the number is included in the solution, while a closed circle indicates that the number is not included.

• An open circle indicates that the number is not included in the solution, while a closed circle indicates that the number is included.

• Both open and closed circles indicate that the number is included in the solution.

• Open circles are used for positive numbers, while closed circles are used for negative numbers.

What does the symbol '>' mean in inequalities?

• It means 'less than'

• It means 'equal to'

• It means 'greater than'

• It means 'not equal to'

What does the symbol '<' mean in inequalities?

• Greater than

• Less than

• Equal to

• Not equal to

What does the symbol '≥' mean in inequalities?

• Less than

• Greater than

• Greater than or equal to

• Equal to

What does the symbol '≤' mean in inequalities?

• Greater than or equal to

• Less than or equal to

• Equal to

• Not equal to

What is a compound inequality?

• A compound inequality consists of two inequalities joined by 'and' or 'or', such as @@x < 3 ext{ or } x > 5@@.

• A compound inequality is a single inequality that combines multiple variables.

• A compound inequality is an equation that has no solutions.

• A compound inequality is a type of polynomial expression.

How do you check if a number is a solution to an inequality?

• By substituting the number into the inequality and checking if the statement is true.

• By comparing the number to the inequality's boundary values.

• By graphing the inequality and seeing if the number lies within the shaded region.

• By calculating the absolute value of the number and comparing it to the inequality.