Sure, let's solve the equation step-by-step to isolate the variable [tex]\( d \)[/tex].
We start with the given equation:
[tex]\[ 2d + 4 = 10 + 5d \][/tex]
The first step is to move all terms involving [tex]\( d \)[/tex] to one side of the equation and the constants to the other side. We'll subtract [tex]\( 5d \)[/tex] from both sides:
[tex]\[ 2d + 4 - 5d = 10 + 5d - 5d \][/tex]
Simplifying this, we get:
[tex]\[ 2d - 5d + 4 = 10 \][/tex]
Which reduces to:
[tex]\[ -3d + 4 = 10 \][/tex]
Next, we move the constant term [tex]\( 4 \)[/tex] to the right side by subtracting [tex]\( 4 \)[/tex] from both sides:
[tex]\[ -3d + 4 - 4 = 10 - 4 \][/tex]
Simplifying this, we obtain:
[tex]\[ -3d = 6 \][/tex]
Finally, to solve for [tex]\( d \)[/tex], we divide both sides by [tex]\(-3\)[/tex]:
[tex]\[ d = \frac{6}{-3} \][/tex]
Simplifying the fraction, we get:
[tex]\[ d = -2 \][/tex]
Thus, the solution to the equation [tex]\( 2d + 4 = 10 + 5d \)[/tex] is:
[tex]\[ d = -2 \][/tex]
