Answer :

To solve the equation [tex]\(8.4x - 98.6 = -1.2x + 35.8\)[/tex], follow these steps:

1. Start by moving all terms involving [tex]\(x\)[/tex] to one side of the equation. To do this, add [tex]\(1.2x\)[/tex] to both sides:

[tex]\[
8.4x + 1.2x - 98.6 = 35.8
\][/tex]

This simplifies to:

[tex]\[
9.6x - 98.6 = 35.8
\][/tex]

2. Next, move the constant term [tex]\(-98.6\)[/tex] to the other side by adding [tex]\(98.6\)[/tex] to both sides:

[tex]\[
9.6x = 35.8 + 98.6
\][/tex]

Simplifying the right side gives:

[tex]\[
9.6x = 134.4
\][/tex]

3. Finally, solve for [tex]\(x\)[/tex] by dividing both sides by [tex]\(9.6\)[/tex]:

[tex]\[
x = \frac{134.4}{9.6}
\][/tex]

Performing the division yields:

[tex]\[
x = 14
\][/tex]

Thus, the solution to the equation is [tex]\(x = 14\)[/tex].

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