Solving Linear Inequalities

The video tutorial covers solving inequalities, starting with basic steps like isolating variables and combining like terms. It progresses to more complex techniques involving distribution and graphing solutions. The tutorial emphasizes checking answers and understanding the direction of shading on graphs. Advanced techniques for solving inequalities are also discussed, ensuring a comprehensive understanding of the topic.

What is the first step in solving the inequality 5x + 4x ≤ 0?

• Subtract 4x from both sides

• Combine like terms

• Add 4 to both sides

• Divide by 5

After combining like terms in the inequality 5x + 4x ≤ 0, what is the next step?

• Multiply both sides by 9

• Divide both sides by 9

• Add 9 to both sides

• Subtract 9 from both sides

When graphing the solution to x ≤ 0, what type of circle is used?

• Open circle

• Closed circle

• No circle

• Half circle

In the inequality -3 > x - 3x - 1, what is the result of combining like terms?

• 2x

• -2x

• 4x

• -4x

What must you remember to do when dividing both sides of an inequality by a negative number?

• Subtract 1 from both sides

• Multiply by 2

• Flip the inequality sign

• Add 1 to both sides

What is the solution to the inequality 1 < x?

• x ≥ 1

• x ≤ 1

• x > 1

• x < 1

In the inequality 3 - 6x + 6 ≤ 6x - 39, what is the first step?

• Subtract 6x from both sides

• Add 39 to both sides

• Add 6x to both sides

• Distribute the negative 6

What is the result of adding 6x to both sides of the inequality 9 - 6x ≤ 6x - 39?

• 9 ≠ 12x - 39

• 9 = 12x - 39

• 9 ≥ 12x - 39

• 9 ≤ 12x - 39

What is the solution to the inequality 4 ≤ x?

• x > 4

• x < 4

• x ≥ 4

• x ≤ 4

What does it mean if an inequality simplifies to a true statement like -2 ≤ 3?

• Only negative numbers are solutions

• All real numbers are solutions

• Only positive numbers are solutions

• No solution