Question

Jill solves the equation 3(x - 5) + 2x = 0. Fill in the blanks for each step with the correct values:
3x + _______ + 2x = 0
5x = _______
x = _______
Options: -1, 15, -5, 3, 1, 5, -3, -15

Answer 1

Let's solve the equation step by step.

Starting with the equation:

\[ 3(x - 5) + 2x = 0 \]

1. **Distribute \(3\) to \(x - 5\)**:
\[ 3x - 15 + 2x = 0 \]

Now we can fill in the first blank as \(-15\):

\[ 3x + \underline{-15} + 2x = 0 \]

2. **Combine like terms**:
\[ 3x + 2x - 15 = 0 \]
\[ 5x - 15 = 0 \]

Now we can fill in the second blank as \(15\):

\[ 5x = \underline{15} \]

3. **Solve for \(x\)**:
\[ 5x = 15 \]
\[ x = \frac{15}{5} \]
\[ x = 3 \]

Now we can fill in the last blank as \(3\):

\[ x = \underline{3} \]

Putting it all together, we have:
- The first blank is \(-15\)
- The second blank is \(15\)
- The third blank is \(3\)

So, the completed steps are:
1. \(3x + \underline{-15} + 2x = 0\)
2. \(5x = \underline{15}\)
3. \(x = \underline{3}\)

Answer 2

are you sure this answer is correct

Answer 3

Yes, let’s verify the steps for solving the equation \(3(x - 5) + 2x = 0\) to ensure accuracy:

1. **Start with the original equation**:
\[
3(x - 5) + 2x = 0
\]

2. **Distribute \(3\) in the first term**:
\[
3x - 15 + 2x = 0
\]

At this point, we can see that:
- The equation can be written as:
\[
3x + (-15) + 2x = 0
\]
So the first blank is indeed **\(-15\)**.

3. **Combine like terms**:
\[
3x + 2x - 15 = 0
\]
which simplifies to:
\[
5x - 15 = 0
\]

Therefore, we can fill in the second blank:
\[
5x = 15
\]
So the second blank is **\(15\)**.

4. **Isolating \(x\)**:
\[
5x = 15 \implies x = \frac{15}{5} = 3
\]

Thus, the third blank is **\(3\)**.

Putting everything together again:
- In the first blank, the answer is **-15**.
- In the second blank, the answer is **15**.
- In the third blank, the answer is **3**.

This solution and the filling of the blanks are all correct. If you have any further questions or need additional clarifications, feel free to ask!