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Look at the equation below.

-10x+13+12=5x-8

Which of the following steps could be used to transform the equation into the form z = a, where a is a number, to show that the equation has one solution?

Select TWO options that apply.

(2 points)

Subtract 13 from both sides of the equation and then simplify.

Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.

Add 8 to both sides of the equation and then simplify

Subtract 10x from both sides of the equation and then simplify

Add 5x to both sides of the equon and then simplify

1 answer

To transform the equation \(-10x + 13 + 12 = 5x - 8\) into the form \(z = a\), we want to isolate \(x\) and then see if we arrive at a single solution.

Let's evaluate the options provided:

  1. Subtract 13 from both sides of the equation and then simplify.

    • This step is valid. By subtracting 13, you would simplify the left side and could prepare for further operations.

  2. Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.

    • This step is not valid in the context of the equation, as we do not have terms labeled 10x or 12x. We have \(-10x\) and \(5x\). This option is incorrect.

  3. Add 8 to both sides of the equation and then simplify.

    • This step is valid. Adding 8 to both sides would help simplify the equation and move towards isolating \(x\).

  4. Subtract 10x from both sides of the equation and then simplify.

    • This step is also valid. Subtracting \(-10x\) (or adding \(10x\)) from both sides would bring all \(x\) terms to one side of the equation, helping to isolate \(x\).

  5. Add 5x to both sides of the equation and then simplify.

    • This step is valid as well. By adding \(5x\) to both sides, you will move all \(x\) terms to one side of the equation.

Based on the options:

The two suitable options to help transform the equation are:

  • Subtract 13 from both sides of the equation and then simplify.
  • Add 8 to both sides of the equation and then simplify.

(Note that the combination of like terms does not apply because error exists in it.)

So, you can choose any two from the valid transformations identified above.