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10x−12−8x=4x+15



What is a step that can be used to transform the equation into the form x = a, where z is a number, to show that the equation has one solution? Select TWO options that apply.

(1 point)
Responses

Subtract 15 from both sides of the equation and then simplify
Subtract 15 from both sides of the equation and then simplify

Combine 10x and 8x to get 18x and then subtract 18x from both sides of the equation
Combine 10x and 8x to get 18x and then subtract 18x from both sides of the equation

add 4x to both sides of the equation and then simplify
add 4x to both sides of the equation and then simplify

Add 12 to both sides of the equation and then simplify
Add 12 to both sides of the equation and then simplify

Subtract 8x from both sides of the equation

3 answers

To transform the equation \(10x - 12 - 8x = 4x + 15\) into the form \(x = a\) (where \(a\) is a number) and show that it has one solution, you can perform the following two steps:

  1. Subtract \(8x\) from both sides of the equation: This allows you to combine like terms on the left side.

    \[10x - 8x - 12 = 4x + 15\]

  2. Add \(12\) to both sides of the equation and then simplify: This helps to isolate the term with \(x\) and remove the constant on the left.

    \[10x - 8x = 4x + 15 + 12\]

Thus, the two options that apply here are:

  • Subtract 8x from both sides of the equation
  • Add 12 to both sides of the equation and then simplify
disagree
You need to subtract 4x and add 12 and simplify

Let's go through the equation step by step to clarify the transformations needed to solve it:

The original equation is: \[ 10x - 12 - 8x = 4x + 15 \]

  1. Combine \(10x\) and \(-8x\) on the left side: \[ (10x - 8x) - 12 = 4x + 15 \] This simplifies to: \[ 2x - 12 = 4x + 15 \]

  2. To isolate \(x\), you can subtract \(4x\) from both sides: \[ 2x - 4x - 12 = 15 \] This simplifies to: \[ -2x - 12 = 15 \]

  3. Now, add \(12\) to both sides: \[ -2x = 15 + 12 \] This simplifies to: \[ -2x = 27 \]

  4. Finally, divide by \(-2\) to solve for \(x\): \[ x = -\frac{27}{2} \]

So, you are correct that subtracting \(4x\) and adding \(12\) are steps that can be used.

The steps from the options that are relevant for transforming the equation are:

  • Subtract \(4x\) from both sides of the equation and then simplify
  • Add \(12\) to both sides of the equation and then simplify

Thank you for your clarification! If you have more questions or need further explanation, feel free to ask.