To solve the problem where 5 less than a number is equivalent to 1 more than three times the number, we can follow these detailed steps:
1. Let the unknown number be [tex]\( x \)[/tex].
2. Translate the word problem into an algebraic equation:
[tex]\[
x - 5 = 3x + 1
\][/tex]
3. Isolate the variable [tex]\( x \)[/tex] on one side of the equation. Start by moving all terms involving [tex]\( x \)[/tex] to one side and constants to the other side:
[tex]\[
x - 5 - 3x = 3x + 1 - 3x
\][/tex]
Simplify both sides:
[tex]\[
x - 3x - 5 = 1
\][/tex]
4. Combine like terms:
[tex]\[
-2x - 5 = 1
\][/tex]
5. Add 5 to both sides to get the term with [tex]\( x \)[/tex] alone:
[tex]\[
-2x - 5 + 5 = 1 + 5
\][/tex]
[tex]\[
-2x = 6
\][/tex]
6. Divide both sides by -2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{6}{-2} = -3
\][/tex]
Therefore, the number is [tex]\( -3 \)[/tex].
