#### Answer

False

#### Work Step by Step

RECALL:
$|a| = k \longrightarrow a = k \text{ or } a = -k$
Use the rule above to obtain:
$|x-1| = 4 \longrightarrow x-1 = 4 \text{ or } x - 1 = -4$
Solve each equation to obtain:
$x-1 = 4 \text{ or } x - 1 = -4
\\x = 4+1 \text{ or } x = -4+1
\\x = 5 \text{ or } x = -3$
Thus, the solution set of the given equation is $\left\{-3, 5\right\}$.
Therefore, the given statement is false.