Solving Multistep Inequalities Challenge

This video tutorial covers solving multi-step inequalities, similar to solving multi-step equations but with comparisons instead of equalities. It explains the process of simplifying inequalities, using inverse operations, and graphing solutions. The tutorial also emphasizes checking solutions by substituting values and ensuring the graph direction is correct. Key concepts include the importance of flipping inequality signs when multiplying or dividing by negative numbers.

What is the first step in solving the inequality 7(x + 3) < 28?

• Subtract 3 from both sides

• Distribute the 7

• Divide both sides by 7

• Combine like terms

When isolating the variable, what is the additive inverse of 21?

• 21

• -7

• -21

• 0

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

• Flip it

• Leave it unchanged

• Subtract 1 from it

• Add 1 to it

How do you represent x < 1 on a graph?

• An open circle at 1 with an arrow pointing right

• A closed circle at 1 with an arrow pointing right

• An open circle at 1 with an arrow pointing left

• A closed circle at 1 with an arrow pointing left

Which of the following is a correct way to check if a solution to an inequality is valid?

• Plugging in a value less than the solution

• Plugging in any random value

• Plugging in a value greater than the solution

• Plugging in the exact solution

In the inequality t/3 ≥ -2, what is the next step after isolating t?

• Divide both sides by 3

• Subtract 2 from both sides

• Multiply both sides by 3

• Add 2 to both sides

What is the result of combining the terms -3 and 10?

• -13

• 13

• -7

• 7

If 4w - 24 < -12, what is the first step to isolate w?

• Subtract 24 from both sides

• Divide both sides by 4

• Add 24 to both sides

• Multiply both sides by 4

In the inequality 5x + 7 ≤ 32, what is the value of x?

• x ≥ 5

• x ≥ 6

• x ≤ 6

• x ≤ 5

What should you do if you divide both sides of an inequality by a negative number?

• Add the same negative number to both sides

• Subtract the same negative number from both sides

• Leave the inequality sign unchanged

• Flip the inequality sign