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------------------------------------------------ Solve for [tex]$c$[/tex].

[tex]$4.74 - 30c = -43 - 82c - 4.26$[/tex]

We start with the equation

[tex]$$
4.74 - 30c = -43 - 82c - 4.26.
$$[/tex]

Step 1. Combine constant terms on the right side

Combine [tex]$$-43$$[/tex] and [tex]$$-4.26$$[/tex]:

[tex]$$
-43 - 4.26 = -47.26.
$$[/tex]

Thus the equation becomes

[tex]$$
4.74 - 30c = -47.26 - 82c.
$$[/tex]

Step 2. Isolate the terms with [tex]$$c$$[/tex]

Add [tex]$$82c$$[/tex] to both sides to move the variable terms to the left side:

[tex]$$
4.74 - 30c + 82c = -47.26 - 82c + 82c,
$$[/tex]

which simplifies to

[tex]$$
4.74 + 52c = -47.26.
$$[/tex]

Step 3. Isolate [tex]$$c$$[/tex]

Subtract [tex]$$4.74$$[/tex] from both sides:

[tex]$$
4.74 + 52c - 4.74 = -47.26 - 4.74,
$$[/tex]

resulting in

[tex]$$
52c = -52.
$$[/tex]

Step 4. Solve for [tex]$$c$$[/tex]

Divide both sides by [tex]$$52$$[/tex]:

[tex]$$
c = \frac{-52}{52}.
$$[/tex]

Simplify the fraction:

[tex]$$
c = -1.
$$[/tex]

Thus, the solution is [tex]$$c = -1.$$[/tex]