To solve the inequality [tex]\( 2d - 10 \leq 3d - 7 \)[/tex] for [tex]\( d \)[/tex], we will go through the following steps:
1. Start with the given inequality:
[tex]\[
2d - 10 \leq 3d - 7
\][/tex]
2. Subtract [tex]\( 2d \)[/tex] from both sides to isolate [tex]\( d \)[/tex] on one side of the inequality:
[tex]\[
-10 \leq d - 7
\][/tex]
3. Add 7 to both sides to further isolate [tex]\( d \)[/tex]:
[tex]\[
-10 + 7 \leq d
\][/tex]
[tex]\[
-3 \leq d
\][/tex]
This simplifies to:
[tex]\[
d \geq -3
\][/tex]
So, the solution to the inequality [tex]\( 2d - 10 \leq 3d - 7 \)[/tex] is [tex]\( d \geq -3 \)[/tex].
Thus, the answer in simplest form is:
[tex]\[
d \geq -3
\][/tex]
