Which is the most efficient first step to solve for [tex] x [/tex] in the equation [tex] 3.7x - 18 = -4.3x - 34 [/tex]?

A. Add [tex] 3.7x [/tex] to both sides of the equation.
B. Add [tex] 4.3x [/tex] to both sides of the equation.
C. Subtract 18 from both sides of the equation.
D. Subtract 34 from both sides of the equation.



Answer :

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.