Jill solves the equation 3(x−5)+2x=0

Question

. Fill in the blanks for each step with the correct values:

Answer 1

To solve the equation \( 3(x - 5) + 2x = 0 \), we can break it down step by step and fill in the blanks as we go.

1. Distribute the \(3\):
   \(3(x - 5) = 3x - 15\)
   Therefore, the equation becomes: \[ 3x - 15 + 2x = 0 \]

2. Combine like terms:
   Combine \(3x\) and \(2x\): \[ (3x + 2x) - 15 = 0 \rightarrow 5x - 15 = 0 \]

3. Add \(15\) to both sides:
   \[ 5x - 15 + 15 = 0 + 15 \rightarrow 5x = 15 \]

4. Divide both sides by \(5\):
   \[ \frac{5x}{5} = \frac{15}{5} \rightarrow x = 3 \]

So, filling in the blanks, the steps can be summarized as follows:

1. Distribute: \(3(x - 5) \rightarrow 3x - 15\)
2. Combine like terms: \(3x - 15 + 2x \rightarrow 5x - 15\)
3. Add \(15\): \(5x - 15 = 0 \rightarrow 5x = 15\)
4. Divide by \(5\): \(x = 3\)

Final answer: \(x = 3\).

Answer 2

3x+______+ 2x = 0

5x = ___________

x = ______________

Answer 3

Let's fill in the blanks step by step for the problem:

1. From the equation \( 3(x - 5) + 2x = 0 \), after distributing \(3\): \[ 3x + ______ + 2x = 0 \] The blank should be \(-15\) from the distribution: \[ 3x - 15 + 2x = 0 \] So, the first blank is -15.

2. Combining like terms gives us: \[ 5x = ______ \] Adding \(15\) to both sides of the equation (after combining \(3x\) and \(2x\)): \[ 5x - 15 = 0 \implies 5x = 15 \] So the second blank is 15.

3. Solving for \(x\): \[ x = ______ \] Dividing both sides by \(5\): \[ x = 3 \]

Thus, the filled blanks are:

1. \(3x + \underline{-15} + 2x = 0\)
2. \(5x = \underline{15}\)
3. \(x = \underline{3}\)