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-15x+24+16x=3x-24

What is a step that can 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.A.
combine like terms 15x and 16x to get 31x and then subtract 31x from both sides of the equation

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

C. subtract 24 from both sides of the equation and then simplify

D. add 3x to both sides of the equation and then simplify

E. add 24 to both sides of the equation and then simplify

1 answer

To transform the equation \(-15x + 24 + 16x = 3x - 24\) into the form \(x = a\), we want to manipulate both sides appropriately.

Let's evaluate the options:

  1. A. combine like terms 15x and 16x to get 31x and then subtract 31x from both sides of the equation.

    • This option is incorrect because you don't combine terms correctly here; you should combine \(-15x\) and \(16x\) (not both as positive) and then perform operations accordingly.

  2. B. subtract 15x from both sides of the equation and then simplify.

    • This option is valid. Subtracting \(15x\) from both sides will help isolate \(x\).

  3. C. subtract 24 from both sides of the equation and then simplify.

    • This option is useful for simplifying terms on both sides but does not directly contribute to isolating \(x\).

  4. D. add 3x to both sides of the equation and then simplify.

    • This option is valid. Adding \(3x\) to both sides will also help isolate \(x\).

  5. E. add 24 to both sides of the equation and then simplify.

    • While this helps simplify \(24\) and contribute to isolating \(x\), we should focus on isolating \(x\) directly through balancing.

The two correct options from what we have are B and D.

Thus, the answer is: B and D.