To solve the linear equation [tex]\( d - 10 - 2d + 7 = 8 + d - 10 - 3d \)[/tex], let's break it down step by step.
1. Combine like terms on both sides of the equation:
On the left side,
[tex]\[
d - 10 - 2d + 7 = (d - 2d) + (-10 + 7) = -d - 3
\][/tex]
On the right side,
[tex]\[
8 + d - 10 - 3d = (8 - 10) + (d - 3d) = -2 - 2d
\][/tex]
2. Rewrite the simplified equation:
[tex]\[
-d - 3 = -2 - 2d
\][/tex]
3. Isolate the variable [tex]\( d \)[/tex] on one side:
Add [tex]\( 2d \)[/tex] to both sides to combine the variable terms:
[tex]\[
-d + 2d - 3 = -2
\][/tex]
Which simplifies to:
[tex]\[
d - 3 = -2
\][/tex]
4. Solve for [tex]\( d \)[/tex]:
Add 3 to both sides:
[tex]\[
d - 3 + 3 = -2 + 3
\][/tex]
[tex]\[
d = 1
\][/tex]
Therefore, the solution to the equation [tex]\( d - 10 - 2d + 7 = 8 + d - 10 - 3d \)[/tex] is
[tex]\[ d = 1 \][/tex]
Among the given options [tex]\( d = -5, d = -1, d = 1, d = 5 \)[/tex], the correct solution is [tex]\( d = 1 \)[/tex].
