Answer :

To solve the equation [tex]\(-53x + 0.5x = -14 - 38.5\)[/tex], we can follow these steps:

1. Combine Like Terms on the Left Side:
The left-hand side of the equation is [tex]\(-53x + 0.5x\)[/tex]. Combine these terms to simplify the equation:
[tex]\[
-53x + 0.5x = -52.5x
\][/tex]

2. Simplify the Right Side:
The right-hand side of the equation is [tex]\(-14 - 38.5\)[/tex]. Combine these terms:
[tex]\[
-14 - 38.5 = -52.5
\][/tex]

3. Equate Both Sides:
Now the equation becomes:
[tex]\[
-52.5x = -52.5
\][/tex]

4. Solve for [tex]\(x\)[/tex]:
Divide both sides by [tex]\(-52.5\)[/tex] to find the value of [tex]\(x\)[/tex]:
[tex]\[
x = \frac{-52.5}{-52.5} = 1
\][/tex]

Therefore, the solution to the equation is [tex]\(x = 1\)[/tex].

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