How many solutions does this equation have?

20d + 15 − 7 = –2(–10d − 4)

Let's solve the equation to determine how many solutions it has:

The given equation is:
\[
20d + 15 - 7 = -2(-10d - 4)
\]

### Step 1: Simplify both sides
First, simplify both sides of the equation.

Left side:
\[
20d + 15 - 7 = 20d + 8
\]

Right side:
Distribute \(-2\) on the right side:
\[
-2(-10d - 4) = 20d + 8
\]

Now, the equation is:
\[
20d + 8 = 20d + 8
\]

### Step 2: Analyze the equation
Subtract \(20d\) from both sides:
\[
8 = 8
\]

This results in a true statement, which indicates that the equation holds for all values of \(d\).

### Conclusion:
Since the equation is true for all values of \(d\), it has **infinitely many solutions**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. What is the difference between equations with no solutions and those with infinitely many solutions?
2. How do you determine if an equation has a unique solution?
3. Can you explain the method to solve linear equations with one variable?
4. How do you verify if a solution to an equation is correct?
5. What happens when solving an equation results in a contradiction, like \(5 = 3\)?

**Tip:** When simplifying equations, always perform the same operation on both sides to maintain equality.

Learn how to solve the equation 20d + 15 - 7 = -2(-10d - 4) with a step-by-step solution. Understand why this equation has infinitely many solutions and how to verify it. Suitable for students in Grades 7-9.

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