What is the solution to the linear equation 10 + 2d + 7 = 8 + 10 + 3d?

To solve the linear equation 10 + 2d + 7 = 8 + 10 + 3d, we will follow these steps:

1. Simplify both sides of the equation:
• On the left side, combine like terms: 10 + 7 = 17, so we have 17 + 2d.
• On the right side, combine like terms: 8 + 10 = 18, so we have 18 + 3d.

This simplifies our equation to:

17 + 2d = 18 + 3d

2. Next, isolate the variable:

To isolate d, we want to get all the d terms on one side and constant terms on the other side. Let’s subtract 2d from both sides:

17 = 18 + d

3. Next, subtract 18 from both sides:

This gives us:

17 – 18 = d which simplifies to -1 = d

4. Conclusion:

The solution to the equation is:

d = -1

Thus, we have found that the value of d that satisfies the equation is -1.