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Look at the equation below.

−10x+13+12x=5x−8

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

Select TWO options that apply.

(2 points)
Responses

Add 5x to both sides of the equation and then simplify.
Add 5x to 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.
Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.

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

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

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

1 answer

To solve the equation \(-10x + 13 + 12x = 5x - 8\), we need to identify two steps that would effectively lead to simplifying the equation.

Let's analyze the provided options one by one:

  1. Add 5x to both sides of the equation and then simplify.
    This does not help isolate \(x\) directly, and additional \(x\) terms on both sides would complicate the equation further. (Not suitable)

  2. Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
    This step does not correctly combine the terms because it misnames the coefficients; \(-10x + 12x\) gives \(2x\), not \(22x\). (Not suitable)

  3. Subtract 13 from both sides of the equation and then simplify.
    This step is valid as it helps in isolating terms involving \(x\). (Suitable)

  4. Subtract 10x from both sides of the equation and then simplify.
    This step is also valid as it directly reduces one of the \(x\) terms, making it easier to combine. (Suitable)

  5. Add 8 to both sides of the equation and then simplify.
    Adding 8 to both sides won't isolate \(x\) directly and does not help progress toward the solution. (Not suitable)

Based on this analysis, the two suitable choices that apply are:

  • Subtract 13 from both sides of the equation and then simplify.
  • Subtract 10x from both sides of the equation and then simplify.