Solving One Variable Inequalities

Solve the inequality: 3(x - 2) < 2(x + 9)

• x < 20

• x < 22

• x < 24

• x < 26

What is the difference between strict and non-strict inequalities?

• Strict inequalities include the boundary point, while non-strict inequalities do not.

• Strict inequalities do not include the boundary point, while non-strict inequalities do include the boundary point.

• Strict inequalities are used only in calculus, while non-strict inequalities are used in algebra.

• Strict inequalities can only be used with integers, while non-strict inequalities can be used with real numbers.

Solve the compound inequality: -3 < 2x + 1 < 5

• -2 < x < 2

• -1 < x < 3

• 0 < x < 4

• -3 < x < 1

How do you graph a solution to an inequality?

• Shade the entire number line without any circles.

• Use a number line and shade the region that represents the solution set, using an open circle for < or > and a closed circle for ≤ or ≥.

• Draw a bar graph to represent the solution set.

• Only use closed circles for all inequalities.

What is the solution to the equation 12x - 14x + 2 = 20 - 6?

• x = 0

• x = -6

• x = 3

• x = 2

What is the importance of understanding inequalities in real life?

• Inequalities help in making decisions based on constraints, such as budgeting, resource allocation, and optimization problems.

• Inequalities are only relevant in theoretical mathematics and have no practical application.

• Inequalities are used to measure the average of a set of numbers.

• Inequalities are primarily concerned with the comparison of two variables without any real-world implications.

How do you check your solution for an inequality?

• Substitute a value from the solution set back into the original inequality to see if it holds true.

• Graph the inequality and check if the solution set is shaded correctly.

• Use a calculator to find the roots of the inequality.

• Check if the inequality is satisfied by testing values outside the solution set.

What is the solution set of an inequality?

• The set of all values that satisfy the inequality.

• A single value that makes the inequality true.

• The range of values that do not satisfy the inequality.

• The set of all possible values for the variable.

What is an inequality?

• A mathematical statement that shows two expressions are equal.

• 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 graphical representation of a function.

What does it mean to solve an inequality?

• To find a single value that satisfies the inequality.

• To find all values of the variable that make the inequality true.

• To determine the maximum value of the variable.

• To graph the inequality on a number line.