Solving Inequalities: Day 1 Insights

What is the key difference between solving equations and solving inequalities?

• Inequalities are always more complex.

• Inequalities require flipping the sign when multiplying or dividing by a negative number.

• There is no difference.

• Equations require more steps.

When solving inequalities, what should you do if there are parentheses?

• Move them to the other side of the inequality.

• Combine them with like terms.

• Ignore them.

• Distribute to remove the parentheses.

In Example 1, what operation is used to isolate the variable x?

• Division

• Addition

• Multiplication

• Subtraction

How do you graph the solution x ≤ -4 on a number line?

• Closed circle at -4, shade to the right.

• Open circle at -4, shade to the right.

• Closed circle at -4, shade to the left.

• Open circle at -4, shade to the left.

In Example 2, what is the first step to isolate the variable y?

• Add 7 to both sides.

• Multiply both sides by 4.

• Subtract 7 from both sides.

• Divide both sides by 4.

How do you rewrite the inequality 4 < y for easier graphing?

• y = 4

• 4 > y

• y > 4

• y < 4

In Example 3, what is the result of combining like terms 2x and 4x?

• 2x

• 4x

• 8x

• 6x

What is the final solution for the inequality 6x - 1 > 17?

• x < 2

• x > 3

• x < 3

• x > 2

In Example 4, what is the first step to simplify the left-hand side with parentheses?

• Add 10 to both sides.

• Combine like terms.

• Distribute 5 to both terms inside the parentheses.

• Subtract 10 from both sides.

What is the final solution for the inequality 5x + 10 ≥ 20?

• x < 2

• x > 2

• x ≤ 2

• x ≥ 2