Solving Inequalities and Their Properties

The video tutorial explains how to solve multi-step inequalities, similar to solving multi-step equations, with the key difference being the reversal of the inequality sign when multiplying or dividing by a negative number. The process involves adding to both sides, rewriting the equation, dividing by a negative, and simplifying to find the solution. The final answer is presented as x greater than or equal to 2.

What is the primary difference between solving a multi-step inequality and a multi-step equation?

• The requirement to solve for y instead of x

• The use of addition and subtraction

• The need to reverse the inequality sign when multiplying or dividing by a negative

• The presence of variables

When solving inequalities, what happens to the inequality sign if you multiply or divide both sides by a negative number?

• It remains the same

• It becomes an equation

• It reverses direction

• It becomes a positive sign

What is the first step in isolating the variable in the inequality -7x ≤ -34?

• Subtract 11 from both sides

• Divide both sides by -7

• Add 11 to both sides

• Multiply both sides by -7

After adding 11 to both sides of the inequality, what is the new inequality?

• -7x ≤ -45

• -7x ≤ -34 + 11

• -7x ≤ -34

• -7x ≤ -23

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

• Subtract the same number from both sides

• Multiply both sides by a positive number

• Reverse the inequality sign

• Add the same number to both sides

What is the result of dividing -34 by -17?

• -2

• 17

• 2

• 0

What is the final solution to the inequality -7x ≤ -34 after all steps are completed?

• x ≤ 2

• x ≥ 2

• x < 2

• x > 2