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Unit 7 Sample Work Retake

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Question
Look at the equation below.
7x-5+4x=15x-9

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 only one solution?

Select TWO options that apply.

Responses

Combine like terms on the left side of the equation to get 6x.
Combine like terms on the left side of the equation to get 6x.

Subtract 9 from both sides of the equation and then simplify.
Subtract 9 from both sides of the equation and then simplify.

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

Add 7x to both sides of the equation and then simplify.
Add 7x to both sides of the equation and then simplify.

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

1 answer

To transform the equation \(7x - 5 + 4x = 15x - 9\) into the form \(x = a\), where \(a\) is a number, the following steps are applicable:

  1. Combine like terms on the left side of the equation to get \(6x\).

    • This step is valid because you need to simplify the left side of the equation.

  2. Subtract \(15x\) from both sides of the equation and then simplify.

    • This step is also valid as it helps move all the terms involving \(x\) to one side of the equation.

Therefore, the correct options to select are:

  • Combine like terms on the left side of the equation to get \(6x\).
  • Subtract \(15x\) from both sides of the equation and then simplify.