How do you solve #4

Question

How do you solve #4< -z -4 < 11#?

Eli Assouline · Accepted Answer

#-15 < z < -8# There are two inequalities here. Firstly, let's solve them. Secondly, we will combine them into a resulting inequality for #z#. #4 < -z - 4# To solve this inequality for #z#, add #z# to both sides of equation and then subtract #4# from both sides. The first transformation will bring positive #z# to the left side instead of negative in the right, getting #z+4 < z-z-4# #z+4 < -4# The second transformation will get rid of #4# on the left: #z+4-4 < -4-4# #z < -8# #-z-4 < 11# To solve this inequality for #z#, add #z# to both sides of equation and then subtract #11# from both sides. The first transformation will bring positive #z# to the right side instead of negative in the left, getting #z-z-4 < z+11# #-4 < z+11# The second transformation will get rid of #11# on the right: #-4-11 < z+11-11# #-15 < z# or, equivalently, #z > -15# So, we have two conditions on #z#: #z < -8# and #z > -15# We can combine them into one: #-15 < z < -8#

Genesis Allen · Answer

undefined To solve the inequality $4 < -z - 4 < 11$, follow these steps: 1. Add 4 to all parts of the inequality: $4 + 4 < -z - 4 + 4 < 11 + 4$ 2. Simplify: $8 < -z < 15$ 3. Multiply all parts of the inequality by -1 to switch the direction of the inequality signs: $-8 > z > -15$ 4. Rewrite the inequality in ascending order: $-15 < z < -8$ So, the solution to the inequality is $-15 < z < -8$.

How do you solve #4&lt; -z -4 &lt; 11#?

How do you solve #4< -z -4 < 11#?