To solve the problem, we need to find the value of the variable [tex]\( c \)[/tex] such that the expression [tex]\( 3 - 5c \)[/tex] is 1 less than the expression [tex]\( 1 - c \)[/tex].
Step-by-Step Solution:
1. Set up the equation based on the given condition:
The problem states that [tex]\( 3 - 5c \)[/tex] is 1 less than [tex]\( 1 - c \)[/tex]. We can write this relationship as:
[tex]\[
3 - 5c = (1 - c) - 1
\][/tex]
2. Simplify the right-hand side of the equation:
Simplify the expression on the right-hand side:
[tex]\[
(1 - c) - 1 = 1 - c - 1 = -c
\][/tex]
3. Rewrite the equation with the simplified right-hand side:
Now, the equation becomes:
[tex]\[
3 - 5c = -c
\][/tex]
4. Combine like terms:
Move all terms involving [tex]\( c \)[/tex] to one side of the equation and constants to the other side:
[tex]\[
3 - 5c + c = 0
\][/tex]
Combine the [tex]\( c \)[/tex] terms:
[tex]\[
3 - 4c = 0
\][/tex]
5. Isolate the variable [tex]\( c \)[/tex]:
Solve for [tex]\( c \)[/tex] by isolating it on one side of the equation:
[tex]\[
-4c = -3
\][/tex]
Divide both sides by -4:
[tex]\[
c = \frac{3}{4}
\][/tex]
Therefore, the value of the variable [tex]\( c \)[/tex] that makes [tex]\( 3 - 5c \)[/tex] 1 less than [tex]\( 1 - c \)[/tex] is [tex]\( \frac{3}{4} \)[/tex].
