How do you solve the absolute value equation #x+absx=28#?

Question

Eva Abramson · Accepted Answer

If #x<0#, the #abs(x)=-x# and #x+absx = 0 !=28# so we must have #x>0# and #absx = x# so we need #x+x=28# and #x=14#

Eva Adamson · Answer

Example: #|-11| = -(-11)# since #-11# is negative and #|-5| = 5# since #5# is already positive. Resuming our inquiry, we have #x + |x| = 28#. Because there are two possible outcomes, #x >=0# or #x<0#, there will only be a maximum of two values for #x#. Case 1: x + x = 28# since #x>=0# x = 14# => 2x = 28# Case 2: # x<0# #=> x - x = 28 => 0 = 28#, but since # 0!= 28# is known, the preceding (final) statement is ambiguous. Thus, #x = 14# is the only value we can keep.

Abigail Allen · Answer

undefined To solve the absolute value equation $ x + |x| = 28 $, you need to consider two cases: when $ x $ is positive and when $ x $ is negative.

1. When $ x \geq 0 $: In this case, $ |x| = x $. So, the equation becomes $ x + x = 28 $, which simplifies to $ 2x = 28 $. Solve for $ x $ to get $ x = 14 $.

2. When $ x < 0 $: In this case, $ |x| = -x $. So, the equation becomes $ x - x = 28 $, which simplifies to $ 0 = 28 $. However, this is not a valid solution because it leads to a contradiction.

Thus, the solution to the absolute value equation $ x + |x| = 28 $ is $ x = 14 $.