How do you solve and graph #abs(p+2)7#?

Question

How do you solve and graph #abs(p+2)>7#?

Genesis Allen · Accepted Answer

See a solution process below:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

#-7 > p + 2 > 7#

Subtract #color(red)(2)# from each segment of the system of inequalities to solve for #p# while keeping the system balanced:

#-7 - color(red)(2) > p + 2 - color(red)(2) > 7 - color(red)(2)#

#-9 > p + 0 > 5#

#-9 > p > 5#

Or

#p < -9# and #p > 5#

To graph this we will draw a vertical lines at #-9# and #5# on the horizontal axis.

The lines will be dashed lines because the inequality operators do not contain "or equal to" clauses.

We will shade to the left and right side of the lines because the inequality operator contains "less than" and "greater than" clauses respectively:

Eva Abramson · Answer

undefined To solve the inequality abs(p + 2) > 7, you need to consider two cases: when p + 2 is positive and when it's negative. 1. When p + 2 is positive: In this case, abs(p + 2) = p + 2, so the inequality becomes: p + 2 > 7 Solve for p: p > 7 - 2 p > 5 2. When p + 2 is negative: In this case, abs(p + 2) = -(p + 2), so the inequality becomes: -(p + 2) > 7 Solve for p: p + 2 < -7 p < -7 - 2 p < -9 Combine the solutions: p > 5 or p < -9 To graph this inequality, you would plot two separate regions on the number line: one for p > 5 and another for p < -9. Then, you would shade each region to indicate the values of p that satisfy the inequality.

How do you solve and graph #abs(p+2)&gt;7#?

How do you solve and graph #abs(p+2)>7#?