Jill solves the equation 3(x−5)+2x=0

Question

Fill in the blanks for each step with the correct values:
3x+_____+2x=0

5x=_____

x=_____

Answer 1

Let's solve the equation step by step:

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

2. Distribute \(3\) in the equation:
   \( 3x - 15 + 2x = 0 \)

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

So, the first blank is filled in with \(-15\):
3x + \(-15\) + 2x = 0

4. Combine \(3x\) and \(2x\):
   \( 5x - 15 = 0 \)

Now, the second blank is filled with \(15\):
5x = \(15\)

5. Isolate \(x\) by adding \(15\) to both sides:
   \( 5x = 15 \)

6. Divide both sides by \(5\):
   \( x = 3 \)

Thus, the final value for \(x\) is:
x = \(3\)

Putting it all together, the filled out statements are:

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