Solving Multi-Step Inequalities in Algebra

The video tutorial explains how to solve the inequality -3p - 7 < p + 9 by isolating the variable p. The process involves subtracting p from both sides, adding 7 to both sides, and dividing by -4, while remembering to reverse the inequality sign. The solution is plotted on a number line, and various values are tested to confirm the solution set. The boundary point is analyzed to ensure it is not included in the solution.

What is the first step to isolate p in the inequality -3p - 7 < p + 9?

• Add 7 to both sides

• Subtract p from both sides

• Divide both sides by -3

• Multiply both sides by -1

After subtracting p from both sides, what is the resulting inequality?

• -4p - 7 < 9

• -3p - 7 < 0

• -4p < 9

• -3p < 9

What operation is performed to eliminate the -7 in the inequality -4p - 7 < 9?

• Add 7 to both sides

• Subtract 7 from both sides

• Multiply both sides by -7

• Divide both sides by -7

What must be done to the inequality sign when dividing both sides by a negative number?

• Change it to an equal sign

• Reverse the inequality sign

• Keep it the same

• Change it to a greater than sign

What is the final solution for p after all simplifications?

• p > -4

• p < -4

• p ≤ -4

• p = -4

Which value of p is part of the solution set?

• -5

• -4

• -3.9999999

• 0

What is the result when p = -3 is substituted back into the original inequality?

• 2 = 6

• 2 > 6

• 2 < 6

• 2 ≤ 6

Why does p = -5 not satisfy the inequality?

• Because 8 is less than 4

• Because 8 is not less than 4

• Because 8 is equal to 4

• Because 8 is greater than 4

What happens when p = -4 is substituted into the original inequality?

• 5 ≤ 5

• 5 < 5

• 5 > 5

• 5 = 5

Why is -4 considered a boundary point in the solution set?

• Because it is greater than the solution set

• Because it satisfies the related equation

• Because it does not satisfy the inequality

• Because it satisfies the inequality