To solve the equation [tex]\(-3 + \frac{4}{5}d + \frac{3}{2}d + 2 = 3d\)[/tex] for [tex]\(d\)[/tex], follow these steps:
1. Combine the constants on the left side of the equation:
First, let’s combine the constant terms [tex]\(-3\)[/tex] and [tex]\(2\)[/tex]:
[tex]\[
-3 + 2 = -1
\][/tex]
So, the equation now looks like:
[tex]\[
-1 + \frac{4}{5}d + \frac{3}{2}d = 3d
\][/tex]
2. Combine the like terms involving [tex]\(d\)[/tex] on the left side:
To combine the coefficients of [tex]\(d\)[/tex], let's first convert them into a common denominator:
[tex]\[
\frac{4}{5}d + \frac{3}{2}d = \frac{8}{10}d + \frac{15}{10}d = \frac{23}{10}d = 2.3d
\][/tex]
Now the equation looks like:
[tex]\[
-1 + 2.3d = 3d
\][/tex]
3. Isolate the term involving [tex]\(d\)[/tex]:
Subtract [tex]\(2.3d\)[/tex] from both sides to move all [tex]\(d\)[/tex]-terms to one side of the equation:
[tex]\[
-1 = 3d - 2.3d
\][/tex]
Simplify the right-hand side:
[tex]\[
-1 = 0.7d
\][/tex]
4. Solve for [tex]\(d\)[/tex]:
Finally, divide both sides by [tex]\(0.7\)[/tex] to isolate [tex]\(d\)[/tex]:
[tex]\[
d = \frac{-1}{0.7} = -1.4285714285714282
\][/tex]
Therefore, the value of [tex]\(d\)[/tex] is [tex]\(d = -1.4285714285714282\)[/tex].
