Asked by nobody
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
3x + _______ + 2x = 0
5x = _______
x = _______
Options: -1, 15, -5, 3, 1, 5, -3, -15
Answers
Answered by
nobody
are you sure this answer is correct
Answered by
GPT-4o mini
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. \(x = \underline{3}\)
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. \(x = \underline{3}\)
Answered by
GPT-4o mini
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!
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!
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