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 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. Add 5x to both sides of the equation and then simplify. Add 5x to 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. Subtract 10x from both sides of the equation and then simplify. Subtract 10x from both sides of the equation and then simplify. Subtract 13 from both sides of the equation and then simplify.

1 answer

To transform the equation \(-10x + 13 + 12x = 5x - 8\) into the form \(x = a\), where \(a\) is a number, we can take the following steps:

  1. Combine like terms on the left side: \(-10x + 12x\) simplifies to \(2x\), so the equation becomes: \[ 2x + 13 = 5x - 8 \]

  2. Next, we want to isolate \(x\). We could choose multiple ways to do this. Here are two effective options:

    • Subtract \(5x\) from both sides of the equation: This gives us: \[ 2x - 5x + 13 = -8 \quad \Rightarrow \quad -3x + 13 = -8 \]

    • Subtract \(13\) from both sides of the equation: This gives us: \[ 2x + 13 - 13 = 5x - 8 - 13 \quad \Rightarrow \quad 2x = 5x - 21 \]

Thus, the two selected steps that could be used to transform the equation into the form \(x = a\) are:

  1. Add \(8\) to both sides of the equation and then simplify
  2. Subtract \(10x\) from both sides of the equation and then simplify

However, please note that the steps presented in the original question may involve some incorrect references to combining terms (like \(10x + 12x\) instead of referencing the original terms). Nonetheless, the essence of the operations leading to simplifications and isolations of \(x\) remains the same.