How do you solve # abs(1 - 3b)= - 7#?

Question

Eli Assouline · Accepted Answer

This equation has no solutions.

We have to start with the definition of the absolute value. The absolute value of a non-negative number is this number itself. Absolute value of the negative number is its negation. In mathematical symbol it looks like that: #X >= 0 => |X|=X# #X < 0 => |X| = -X# Using this definition, let's divide a set of all possible values of #b# into two parts: (a) those where #1-3b >=0# (or #b<=1/3#) (b) those where #1-3b < 0# (or #b>1/3#). In case (a) our equation looks like this: #1-3b = -7#, which has a solution #b=8/3#. This solution does not belong to the area of #b<=1/3# and must be discarded. In case (b) our equation looks like this: #-(1-3b) = -7#, which has a solution #b=-2#. This solution does not belong to the area of #b>1/3# and must be discarded. So, no solutions are found for this equation. We can confirm this graphically by observing that function #y=|1-3x|+7# does not have intersections with X-axis. graph{|1-3x|+7 [-46.23, 46.25, -23.12, 23.1]}

Isaiah Anthony · Answer

exactly no solutions

because #absa# can't be negative, you can't find any solution which satifies this equation

Savannah Anderson · Answer

undefined The absolute value of a number cannot be negative, so there is no solution to the equation abs(1 - 3b) = -7.