To solve for [tex]\( x \)[/tex] in the equation [tex]\( 3.7x - 18 = -4.3x - 34 \)[/tex], the most efficient first step is to add [tex]\( 4.3x \)[/tex] to both sides of the equation. Here is the detailed, step-by-step solution:
1. Write down the original equation:
[tex]\[
3.7x - 18 = -4.3x - 34
\][/tex]
2. Add [tex]\( 4.3x \)[/tex] to both sides to eliminate the [tex]\( -4.3x \)[/tex] term on the right side of the equation:
[tex]\[
3.7x + 4.3x - 18 = -4.3x + 4.3x - 34
\][/tex]
Simplifying gives:
[tex]\[
8x - 18 = -34
\][/tex]
3. Add 18 to both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
8x - 18 + 18 = -34 + 18
\][/tex]
Simplifying gives:
[tex]\[
8x = -16
\][/tex]
4. Divide both sides by 8 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-16}{8}
\][/tex]
Simplifying gives:
[tex]\[
x = -2
\][/tex]
Thus, the most efficient first step is to add [tex]\( 4.3x \)[/tex] to both sides of the equation.
