Chapter 1 - Solving Linear Equations - 1.4 - Solving Absolute Value Equations - Exercises - Page 32: 19

$-3.5, 6$

Given $$|4b - 5| = 19.$$ a) Equate $4b-5$ to $19$ $$4b - 5 = 19.$$ Add $5$ to both sides $$4b = 24.$$ Divide both sides by $4$ $$b = 6.$$ b) Equate $4b-5$ to $-19$ $$4b - 5 = -19.$$ Add $5$ to both sides $$4b = -14.$$ Divide both sides by $4$ $$b =-\frac{14}{4}=-3.5.$$ Hence, the solutions are $-3.5$ and $6$. The solutions are graphed on the number line.