To solve the given inequality, we proceed step by step:
1. Start with the given inequality:
[tex]\[
x - 1 < -4
\][/tex]
2. To isolate [tex]\( x \)[/tex] on one side of the inequality, we need to eliminate the [tex]\(-1\)[/tex] from the left side. We can do this by adding 1 to both sides of the inequality. This will not change the direction of the inequality:
[tex]\[
x - 1 + 1 < -4 + 1
\][/tex]
3. Simplify both sides:
[tex]\[
x < -3
\][/tex]
Thus, the solution to the inequality [tex]\(x - 1 < -4\)[/tex] is [tex]\(x < -3\)[/tex].
To verify the given result [tex]\(x < 5\)[/tex], we need to compare it with our simplified answer:
We concluded that the solution is [tex]\(x < -3\)[/tex]. Since [tex]\(-3\)[/tex] is less than [tex]\(5\)[/tex] and includes values smaller than [tex]\(-3\)[/tex], which are also smaller than [tex]\(5\)[/tex], stating [tex]\(x < 5\)[/tex] is incorrect.
Therefore, the statement "The solution of [tex]\(x-1<-4\)[/tex] is [tex]\(x < 5\)[/tex]" is:
[tex]\[
\text{False}
\][/tex]
