How do you solve and write the following in interval notation: #3 |x + 5| + 6=15#?

Question

How do you solve and write the following in interval notation: #3 |x + 5| + 6>=15#?

Hazel Anglin · Accepted Answer

See a solution process below:

First, subtract #color(red)(6)# from each side of the inequality to isolate the absolute value term while keeping the inequality balanced: #3abs(x + 5) + 6 - color(red)(6) >= 15 - color(red)(6)# #3abs(x + 5) + 0 >= 9# #3abs(x + 5) >= 9# next, divide each side of the inequality by #color(red)(3)# to isolate the absolute value function while keeping the inequality balanced: #(3abs(x + 5))/color(red)(3) >= 9/color(red)(3)# #(color(red)(cancel(color(black)(3)))abs(x + 5))/cancel(color(red)(3)) >= 3# #abs(x + 5) >= 3# We must solve the term within the absolute value function for both its negative and positive equivalent because the absolute value function takes any term, whether positive or negative, and converts it to its positive form. #-3 >= x + 5 >= 3# Now, subtract #color(red)(5)# from each segment of the system of inequalities to solve for #x# while keeping the system balanced: #-3 - color(red)(5) >= x + 5 - color(red)(5) >= 3 - color(red)(5)# #-8 >= x + 0 >= -2# #-8 >= x >= -2# Or #x <= -8# and #x >= -2# Instead, using interval notation: #(-oo, -8]# and #[-2, oo)#

Eva Abramson · Answer

undefined To solve the inequality $3 |x + 5| + 6 \geq 15$, first subtract 6 from both sides, then divide by 3. The solution in interval notation is $x \geq -4$ or $x \leq 4$.

How do you solve and write the following in interval notation: #3 |x + 5| + 6&gt;=15#?

How do you solve and write the following in interval notation: #3 |x + 5| + 6>=15#?