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Fill in the blanks to follow the steps in solving the equation:

5x - 12 - 6x = -10x + 7 - 1
Step 1: Combine like terms ___________
Step 2: Get x-terms on same side of equation ___________
Step 3: Get constants on same side of equation ____________
Step 4: Get the x by itself by using the inverse operation ____________
Options to the question: -1x - 12 = -10x + 6, 5 - 18x = -3x - 1, 1x - 12 = -10x + 6, -12 = -11x + 6, 9x - 12 = 6, -12 = -9x + 6, -18 = 9x, -6 = -9x, -18 = -9x, x = 0, x = 1, x = 2, x = -2

3 answers

Let's go through the steps to fill in the blanks for solving the equation:

  1. Combine like terms: Starting with the original equation: \(5x - 12 - 6x = -10x + 7 - 1\)

    On the left side, combine \(5x\) and \(-6x\): \(-1x - 12\).

    On the right side, simplify \(7 - 1\): \(-10x + 6\).

    So we obtain: \(-1x - 12 = -10x + 6\).

    Step 1: Combine like terms -1x - 12 = -10x + 6.

  2. Get x-terms on the same side of the equation: Add \(10x\) to both sides: \(-1x + 10x - 12 = 6\).

    This simplifies to: \(9x - 12 = 6\).

    Step 2: Get x-terms on the same side of the equation 9x - 12 = 6.

  3. Get constants on the same side of the equation: Add \(12\) to both sides: \(9x = 6 + 12\).

    This simplifies to: \(9x = 18\).

    Step 3: Get constants on the same side of the equation 9x = 18.

  4. Get the x by itself using the inverse operation: Divide both sides by \(9\): \(x = 2\).

    Step 4: Get the x by itself using the inverse operation x = 2.

So overall, filling in the original blanks:

  1. Step 1: Combine like terms -1x - 12 = -10x + 6.
  2. Step 2: Get x-terms on the same side of equation 9x - 12 = 6.
  3. Step 3: Get constants on the same side of the equation 9x = 18.
  4. Step 4: Get the x by itself using the inverse operation x = 2.
are you sure this is correct

Let's go through the steps again clearly and verify the solution for the equation \(5x - 12 - 6x = -10x + 7 - 1\).

  1. Combine like terms:
    Start with the equation:
    \(5x - 12 - 6x = -10x + 7 - 1\)

    On the left side, combine \(5x\) and \(-6x\):
    \((-1)x - 12\)

    On the right side, simplify \(7 - 1\):
    \(-10x + 6\)

    So, we rewrite it as:
    \(-1x - 12 = -10x + 6\).
    Step 1: Combine like terms: -1x - 12 = -10x + 6.

  2. Get x-terms on the same side of the equation:
    Add \(10x\) to both sides:
    \(-1x + 10x - 12 = 6\)
    \(9x - 12 = 6\).
    Step 2: Get x-terms on the same side of the equation: 9x - 12 = 6.

  3. Get constants on the same side of the equation:
    Add \(12\) to both sides:
    \(9x = 6 + 12\)
    \(9x = 18\).
    Step 3: Get constants on the same side of the equation: 9x = 18.

  4. Get the x by itself using the inverse operation:
    Divide both sides by \(9\):
    \(x = \frac{18}{9}\)
    \(x = 2\).
    Step 4: Get the x by itself using the inverse operation: x = 2.

So upon re-evaluating, the steps I provided are indeed correct. Thus, the final answer remains:

  • Step 1: Combine like terms -1x - 12 = -10x + 6,
  • Step 2: Get x-terms on the same side of equation 9x - 12 = 6,
  • Step 3: Get constants on the same side of the equation 9x = 18,
  • Step 4: Get the x by itself using the inverse operation x = 2.

If you have specific doubts or require further explanation on any of the steps, please let me know!