Question

determine d in the equation.
16.4 = -1.2 - 2d
\\( d = -7.6 \\)
\\( d = 7.6 \\)
\\( d = -8.8 \\)
\\( d = 8.8 \\)

Explanation:

Step1: Add 1.2 to both sides

To isolate the term with \( d \), we add \( 1.2 \) to both sides of the equation \( 16.4 = -1.2 - 2d \). This gives us \( 16.4 + 1.2 = -2d \). Calculating the left side, \( 16.4 + 1.2 = 17.6 \), so the equation becomes \( 17.6 = -2d \).

Step2: Divide both sides by -2

Now, to solve for \( d \), we divide both sides of the equation \( 17.6 = -2d \) by \( -2 \). So, \( d=\frac{17.6}{-2} \). Calculating this, we get \( d = -8.8 \). Wait, no, wait. Wait, let's re - check. Wait, the original equation is \( 16.4=-1.2 - 2d \). Let's do it again.

Wait, first, add \( 1.2 \) to both sides: \( 16.4 + 1.2=-2d \), \( 17.6=-2d \). Then divide both sides by - 2: \( d=\frac{17.6}{-2}=-8.8 \)? Wait, no, that's not right. Wait, maybe I made a mistake. Wait, let's start over.

The equation is \( 16.4=-1.2 - 2d \). Let's add \( 2d \) to both sides: \( 16.4 + 2d=-1.2 \). Then subtract \( 16.4 \) from both sides: \( 2d=-1.2 - 16.4 \). \( -1.2-16.4=-17.6 \). So \( 2d=-17.6 \). Then divide both sides by 2: \( d = \frac{-17.6}{2}=-8.8 \). Wait, but let's check the options. One of the options is \( d = - 8.8 \). Wait, but let's verify by plugging back in. If \( d=-8.8 \), then the right - hand side of the original equation is \( -1.2-2\times(-8.8)=-1.2 + 17.6 = 16.4 \), which matches the left - hand side. So the correct value of \( d \) is \( -8.8 \).

Wait, but earlier when I added 1.2 to both sides, I had \( 16.4 + 1.2=-2d \), which is \( 17.6=-2d \), then \( d = 17.6\div(-2)=-8.8 \). Yes, that's correct.

Answer:

\( d=-8.8 \) (the option is \( d = - 8.8 \))