4x Consider the sequence of steps to solve the equation: 2(x - 4) + 6x = 9x - 10

Given → 2(x - 4) + 6x = 9x - 10
Step 1 → 2x - 8+6x =9x-10
Step 2 → 2x + 6x - 8 = 9x - 10
Step 3 → 8x - 8 = 9x - 10
Step 4 → 8x - 8x - 8 = 9x - 8x - 10
Step 5 → 0-8=x-10
Step 6 → -8 = x -10
Step 7 → -8 + 10 = x - 10 + 10
Step 8 → 2 = x + 0
Step 9 → 2 = x
Which step in solving this equation is justified by Combining Like Terms?
4x
A
Step 1 → 2x - 8 + 6x = 9x - 10
Ix
B
Step 2 → 2x + 6x - 8 = 9x - 10
•x
C
Step 3 → 8x - 8 = 9x - 10
Ix
D
Step 4 → 8x - 8x - 8 = 9x - 8x - 10 4x Consider the sequence of steps to solve the equation: 2(x - 4) + 6x = 9x - 10
Given → 2(x - 4) + 6x = 9x - 10
Step 1 → 2x - 8+6x =9x-10
Step 2 → 2x + 6x - 8 = 9x - 10
Step 3 → 8x - 8 = 9x - 10
Step 4 → 8x - 8x - 8 = 9x - 8x - 10
Step 5 → 0-8=x-10
Step 6 → -8 = x -10
Step 7 → -8 + 10 = x - 10 + 10
Step 8 → 2 = x + 0
Step 9 → 2 = x
Which step in solving this equation is justified by Combining Like Terms?
4x
A
Step 1 → 2x - 8 + 6x = 9x - 10
Ix
B
Step 2 → 2x + 6x - 8 = 9x - 10
•x
C
Step 3 → 8x - 8 = 9x - 10
Ix
D
Step 4 → 8x - 8x - 8 = 9x - 8x - 10

1 answer

In this sequence of steps to solve the equation \(2(x - 4) + 6x = 9x - 10\), the step that is specifically justified by combining like terms is:

C

  • Step 3 → \(8x - 8 = 9x - 10\)

In Step 3, you combine the \(2x\) and \(6x\) from the left side to get \(8x\), and the constant terms are kept separate. Additionally, Step 1 already combined like terms to some extent, but it is in Step 3 that the expression is simplified to clearly show the results of combining the terms.

  • Step 1 involves performing the distribution and combining \(2x\) and \(6x\).
  • Step 2 presents the same expression rearranged but doesn't introduce any new like terms.
  • Step 4 does not involve combining like terms; it simplifies by isolating variables.

Therefore, Step 3 is the best answer as it's where the combined like terms clearly show what the equation simplifies to.