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McGraw Hill Glencoe Algebra 1, 2012 – Inequalities Involving Absolute Value

Solution Set: {p | p≤- 6 or p≥ 10}
Graph:

Solution

We are asked to find and graph the solution set for all possible values of p in the given inequality. |p-2|≥ 8 To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number that makes the distance between p and 2 greater than or equal to 8 in the positive direction or in the negative direction. p-2 ≥ 8 or p-2≤ - 8Let's isolate p in both of these cases before graphing the solution set.

Case 1

p-2≥ 8
AddIneq

LHS+2≥RHS+2

p≥ 10

This inequality tells us that all values greater than or equal to 10 will satisfy the inequality.

Case 2

p-2≤- 8
AddIneq

LHS+2≤RHS+2

p≤- 6

This inequality tells us that all values less than or equal to - 6 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& p≥ 10 Second Solution Set:& p≤ - 6 Combined Solution Set:& p≤- 6 or p≥ 10

Graph

The graph of this inequality includes all values less than or equal to - 6 or greater than or equal to 10. We show this by keeping the endpoints closed.

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