Sure, let's solve the equation step-by-step.
Given the equation:
[tex]\[ 3 + 4d - 14 = 15 - 5d - 4d \][/tex]
1. Combine like terms on each side of the equation:
[tex]\[
3 - 14 + 4d = 15 - (5d + 4d)
\][/tex]
Simplifying both sides:
[tex]\[
3 - 14 = -11
\][/tex]
[tex]\[
15 - 5d - 4d = 15 - 9d
\][/tex]
Now the equation looks like:
[tex]\[
-11 + 4d = 15 - 9d
\][/tex]
2. Add 9d to both sides to collect all the \(d\)-terms on one side:
[tex]\[
-11 + 4d + 9d = 15
\][/tex]
Simplifying the left side:
[tex]\[
4d + 9d = 13d
\][/tex]
Now the equation is:
[tex]\[
13d - 11 = 15
\][/tex]
3. Add 11 to both sides to isolate the term with \(d\) on one side:
[tex]\[
13d - 11 + 11 = 15 + 11
\][/tex]
Simplifying the right side:
[tex]\[
15 + 11 = 26
\][/tex]
Now the equation is:
[tex]\[
13d = 26
\][/tex]
4. Divide both sides by the coefficient of \(d\), which is 13, to solve for \(d\):
[tex]\[
d = \frac{26}{13}
\][/tex]
5. Simplify the fraction:
[tex]\[
d = 2
\][/tex]
So, the solution to the equation \(3 + 4d - 14 = 15 - 5d - 4d\) is:
[tex]\[
d = 2
\][/tex]
The steps in order are:
1. Combine like terms.
2. Add 9d to both sides.
3. Add 11 to both sides to isolate the term with \(d\).
4. Divide both sides by 13.
5. Simplify the fraction.
Hence, [tex]\(d = 2\)[/tex].
