Question

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

3x + Blank + 2x = 0
5x= (Blank)

x= (Blank)

Answer 1

Let's solve the equation step-by-step.

Starting with:
\[ 3(x−5)+2x=0 \]

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

Now, we can fill in the blanks:

**First Blank: -15** (the result after distributing)

Thus, we have:
\[ 3x - 15 + 2x = 0 \]

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

Now, we can fill in the second blank:

**Second Blank: 15** (the number after moving 15 to the other side)

Thus, we have:
\[ 5x = 15 \]

3. Solve for \(x\) by dividing both sides by \(5\):
\[ x = \frac{15}{5} \]
\[ x = 3 \]

Now, we can fill in the third blank:

**Third Blank: 3** (the value of \(x\))

Putting it all together:

- First Blank: **-15**
- Second Blank: **15**
- Third Blank: **3**