Solving Multi-Step Inequalities Challenge

This video tutorial covers solving multi-step inequalities, graphing them, and writing them in interval notation. It explains interval notation, including the use of brackets and parentheses, and provides examples to illustrate the concepts. The tutorial also discusses the steps for solving inequalities, highlighting the differences from solving equations, such as the need to flip the inequality symbol when multiplying or dividing by a negative number. Four examples are provided, each demonstrating the process of solving and graphing inequalities, with a focus on understanding interval notation.

What are the three main topics covered in the video tutorial?

• Solving equations, graphing them, and writing them in standard form

• Solving multi-step inequalities, graphing them, and writing them in interval notation

• Solving single-step inequalities, graphing them, and writing them in set notation

• Solving quadratic equations, graphing them, and writing them in interval notation

What does interval notation help us represent?

• The graph of a quadratic function

• The steps to solve an equation

• The range of answers for an inequality

• The exact solution to an equation

Which symbol is used in interval notation to represent an open circle on a graph?

• Square bracket

• Curly brace

• Parenthesis

• Bracket

What is the main goal when solving an inequality?

• To get the variable alone

• To find the exact value of the variable

• To graph the inequality

• To write the inequality in standard form

What must you do to the inequality symbol when you multiply or divide by a negative number?

• Change it to an equal sign

• Remove it

• Leave it unchanged

• Flip it

In Example A, what operation is performed to both sides of the inequality x / -4 < 2?

• Division

• Multiplication

• Subtraction

• Addition

What is the interval notation for the solution to Example A: x / -4 < 2?

• (-∞, -8]

• (-8, ∞)

• (-∞, -8)

• (-8, ∞]

In Example B, what is the first step to solve the inequality 3A - 7 ≥ 11?

• Add 7 to both sides

• Subtract 7 from both sides

• Divide both sides by 3

• Multiply both sides by 3

In Example C, what is the result of distributing -1 into the parentheses of 7t - (t + 4)?

• 7t + t - 4

• 7t - t + 4

• 7t + t + 4

• 7t - t - 4

In Example D, what is the final solution to the inequality 4X - 9 > 2X + 1?

• X ≤ 5

• X ≥ 5

• X < 5

• X > 5