To solve the equation [tex]\(3.7x - 18 = -4.3x - 34\)[/tex] for [tex]\(x\)[/tex]:
1. Identify the terms involving [tex]\(x\)[/tex] on both sides of the equation. You have [tex]\(3.7x\)[/tex] on the left side and [tex]\(-4.3x\)[/tex] on the right side.
2. To simplify the equation, it's generally useful to combine like terms involving [tex]\(x\)[/tex]. One efficient way to do this is by moving all [tex]\(x\)[/tex]-terms to one side of the equation.
3. To eliminate the [tex]\(-4.3x\)[/tex] on the right side, we can add [tex]\(4.3x\)[/tex] to both sides of the equation. This step will help to consolidate all the [tex]\(x\)[/tex]-terms on one side.
Here's the step-by-step approach:
[tex]\[
3.7x - 18 = -4.3x - 34
\][/tex]
First Step: Add [tex]\(4.3x\)[/tex] to both sides of the equation:
[tex]\[
3.7x + 4.3x - 18 = -4.3x + 4.3x - 34
\][/tex]
This simplifies to:
[tex]\[
8x - 18 = -34
\][/tex]
Therefore, the most efficient first step to solve for [tex]\(x\)[/tex] in the equation [tex]\(3.7x - 18 = -4.3x - 34\)[/tex] is to add [tex]\(4.3x\)[/tex] to both sides of the equation.
