Solving Multi-Step Inequalities Challenge

The video tutorial explains how to solve multi-step inequalities, which involve both addition or subtraction and multiplication or division. It highlights the importance of distributing, combining like terms, and reversing operations. The tutorial provides four examples: solving inequalities, identifying no solution cases, and recognizing when all real numbers are solutions. Key points include changing the inequality direction when multiplying or dividing by a negative number.

What must you remember to do when you multiply or divide an inequality by a negative number?

• Keep the inequality sign the same

• Change the direction of the inequality sign

• Subtract the same number from both sides

• Add the same number to both sides

In the inequality 5 - 10X > 45, what is the first step to isolate the variable X?

• Divide both sides by -10

• Multiply both sides by 10

• Subtract 5 from both sides

• Add 10 to both sides

After isolating the variable in the inequality 5 - 10X > 45, what is the solution for X?

• X < -4

• X > -4

• X < 4

• X > 4

In the inequality 4(3X - 5) + 7 ≤ 8X + 3, what is the first step?

• Add 5 to both sides

• Subtract 7 from both sides

• Distribute the 4

• Combine like terms

What is the solution to the inequality 4(3X - 5) + 7 ≤ 8X + 3 after isolating the variable?

• X < 4

• X > 4

• X ≥ 4

• X ≤ 4

In the inequality 9X - 5(X - 5) < 4(X - 3), what do you get after distributing and combining like terms?

• 4X + 25 < 4X - 12

• 4X - 25 < 4X + 12

• 9X + 25 < 4X + 12

• 9X - 25 < 4X - 12

What is the conclusion when you solve the inequality 9X - 5(X - 5) < 4(X - 3) and get 25 < -12?

• X must be positive

• There is no solution

• X must be negative

• X can be any number

In the inequality 3(4X + 6) ≤ 42 + 6(2X - 4), what is the first step?

• Subtract 6 from both sides

• Distribute the 3

• Combine like terms

• Add 42 to both sides

What do you notice when you solve the inequality 3(4X + 6) ≤ 42 + 6(2X - 4) and get 18 ≤ 18?

• X can be any number

• There is no solution

• X must be positive

• X must be negative

What is a key step in solving multi-step inequalities?

• Always add the same number to both sides

• Always subtract the same number from both sides

• Distribute and combine like terms

• Ignore the inequality sign