To solve the equation [tex]\(7d - 4 = 3d + 5\)[/tex], we need to isolate the variable [tex]\(d\)[/tex]. Here is a detailed, step-by-step solution:
1. Start with the given equation:
[tex]\[
7d - 4 = 3d + 5
\][/tex]
2. Move all the terms involving [tex]\(d\)[/tex] to one side of the equation. To do this, subtract [tex]\(3d\)[/tex] from both sides:
[tex]\[
7d - 3d - 4 = 5
\][/tex]
Simplifying the left-hand side, we get:
[tex]\[
4d - 4 = 5
\][/tex]
3. Move the constant term to the other side of the equation. To do this, add 4 to both sides:
[tex]\[
4d - 4 + 4 = 5 + 4
\][/tex]
Simplifying both sides, we get:
[tex]\[
4d = 9
\][/tex]
4. Now, solve for [tex]\(d\)[/tex] by dividing both sides of the equation by 4:
[tex]\[
d = \frac{9}{4}
\][/tex]
5. Convert the fraction to a decimal, if needed:
[tex]\[
d = 2.25
\][/tex]
So, the solution to the equation [tex]\(7d - 4 = 3d + 5\)[/tex] is:
[tex]\[
d = 2.25
\][/tex]
