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

Question

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!