Two-Step Inequalities

What does it mean to graph an inequality?

• Graphing an inequality means representing the solution set on a number line, using open or closed circles to indicate whether endpoints are included.

• Graphing an inequality involves drawing a straight line that represents the equation of the inequality.

• Graphing an inequality means plotting points that satisfy the inequality on a coordinate plane.

• Graphing an inequality requires finding the intersection of two different inequalities.

What does the inequality @@x \geq 0@@ represent?

• It represents all non-negative numbers, including zero.

• It represents all negative numbers.

• It represents only positive numbers.

• It represents all real numbers.

How do you solve the inequality @@2 - 3x \leq 20@@?

• Subtract 2 from both sides: @@-3x \leq 18@@, then divide by 3: @@x \leq -6@@.

• Subtract 2 from both sides: @@-3x \leq 18@@, then divide by -3 (flip the sign): @@x \geq -6@@.

• Add 3x to both sides: @@2 \leq 20 + 3x@@, then divide by 3: @@x \leq 6@@.

• Add 2 to both sides: @@-3x \geq 22@@, then divide by -3 (flip the sign): @@x \leq -rac{22}{3}@@.

What is a two-step inequality?

• A type of inequality that requires only one operation to solve.

• An inequality that requires two operations to isolate the variable, typically involving addition or subtraction followed by multiplication or division.

• An equation that has two variables and requires two steps to solve.

• A simple inequality that can be solved in one step.

How do you solve the inequality @@25 < X - 10@@?

• Add 10 to both sides: @@X > 35@@

• Subtract 10 from both sides: @@X < 15@@

• Multiply both sides by 2: @@50 < 2X - 20@@

• Divide both sides by 5: @@5 < X - 2@@

What is the solution to the inequality @@x - 5 < 3@@?

• @@x < 8@@

• @@x > 8@@

• @@x < 2@@

• @@x = 8@@

What is the solution to the inequality @@x + 4 < 10@@?

• @@x < 6@@

• @@x > 6@@

• @@x = 6@@

• @@x < 4@@

• It means that x can be any number greater than 5, but not 5 itself.

• It means that x can be exactly 5.

• It means that x can be any number less than 5.

• It means that x can be any number greater than or equal to 5.

What does the inequality @@X \leq 10@@ represent on a number line?

• It represents all numbers greater than 10.

• It represents all numbers less than 10, excluding 10 itself.

• It represents all numbers less than or equal to 10, including 10 itself.

• It represents only the number 10.

What is the difference between @@<@@ and @@\leq@@?

• @@<@@ means 'less than' and does not include the endpoint, while @@\leq@@ means 'less than or equal to' and includes the endpoint.

• @@<@@ means 'less than or equal to' and includes the endpoint, while @@\leq@@ means 'greater than' and does not include the endpoint.

• @@<@@ means 'greater than' and does not include the endpoint, while @@\leq@@ means 'less than' and includes the endpoint.

• @@<@@ means 'less than' and includes the endpoint, while @@\leq@@ means 'less than or equal to' and does not include the endpoint.