How do you solve #abs(2x)

Question

How do you solve #abs(2x)<2+ abs3#?

Eva Adamson · Accepted Answer

First of all, simplify the inequality. Since #|3|=3#, we can rewrite this inequality as #|2x| < 5# Both sides of an inequality can be divided by a positive constant without changing the sign of inequality, and the new inequality will be equivalent to an old one. Let's divide out equation by #2#. The result is: #|x| < 2.5# The solution to this inequality is, obviously, #-2.5 < x < 2.5# The above solution can be obtained using the following logic: By definition, #|x|# is defined as #|x| = x# for all #x>=0# and #|x| = -x# for all #x<0#. Therefore, we can look for solutions of our inequality for #x>=0# and, separately, for #x<0#. Case 1. Assume #x>=0#. Then #|x|=x# and our inequality looks like #x < 2.5#. Combining this with a requirement #x>=0#, we have the following solutions: #0<=x<2.5# Case 2. Assume #x < 0#. Then #|x|=-x# and our inequality looks like #-x < 2.5# or #x > -2.5#.. Combining this with a requirement #x < 0#, we have the following solutions: #-2.5 < x < 0# Combining two areas that represent solutions, #0 <= x < 2.5# and #-2.5 < x < 0#, we obtain one interval for #x# - the solution to our inequality: #-2.5 < x < 2.5#.

Hazel Anglin · Answer

undefined To solve the inequality $ |2x| < 2 + |3| $, follow these steps:

1. Split the absolute value inequalities:
   $ -2 < 2x < 2 + 3 $

2. Simplify the inequality:
   $ -2 < 2x < 5 $

3. Divide each part of the inequality by 2:
   $ -1 < x < \frac{5}{2} $

So, the solution to the inequality is $ -1 < x < \frac{5}{2} $.

How do you solve #abs(2x)&lt;2+ abs3#?

How do you solve #abs(2x)<2+ abs3#?