Solving Linear Inequalities: Example 2 Insights

What type of inequalities are considered more cumbersome compared to linear inequalities?

• Exponential inequalities

• Cubic inequalities

• Logarithmic inequalities

• Quadratic inequalities

What is the result of distributing 5 in the expression 5(x + 3)?

• 5x - 3

• 5x + 15

• 5x + 3

• 5x - 15

After distributing and simplifying, what is the next step to keep the variable positive?

• Subtract 2x from both sides

• Divide both sides by 2

• Add 2x to both sides

• Multiply both sides by 2

What is the inequality after subtracting 15 from both sides?

• 3x ≥ -25

• 3x = -25

• 3x < -25

• 3x ≤ -25

What is the final solution for x after dividing both sides by 3?

• x ≥ -25/3

• x < -25/3

• x = -25/3

• x ≤ -25/3

In interval notation, how is the solution x ≤ -25/3 represented?

• (-∞, -25/3]

• [-25/3, ∞)

• (-25/3, ∞)

• (-∞, -25/3)

What is the purpose of shading in the number line representation?

• To indicate the range of solutions

• To show the midpoint

• To mark the origin

• To highlight the positive numbers

What does the bracket in interval notation indicate?

• The interval is open

• The number is excluded

• The interval is infinite

• The number is included

What does the parenthesis in interval notation indicate?

• The number is excluded

• The number is included

• The interval is closed

• The interval is finite

What is a common mistake people make with interval notation?

• Using negative numbers incorrectly

• Misplacing the variable

• Incorrectly distributing terms

• Forgetting the correct use of brackets and parentheses