Look at the equation shown

-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

1 answer

To transform the equation \(-15x + 24 + 16x = 3x - 24\) into the form \(x = a\) (where \(a\) is a number), we can choose two steps that effectively simplify and combine terms.

Let's assess the options:

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 are mistakenly referring to the combination of \(15x\) and \(16x\) without correcting the negative sign of \(-15x\). You should actually combine \(-15x\) and \(16x\), which results in \(x\), not \(31x\).

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

  • This option is not applicable because we have \(-15x\) and \(16x\) on the left side. You would want to simplify those terms instead.

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

  • This option is valid as it helps eliminate the constant term 24.

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

  • This option is also valid as it can help balance the \(x\) terms.

Thus, the correct two choices that can effectively lead you to \(x = a\) are:

C. Subtract 24 from both sides of the equation and then simplify.
D. Add 3x to both sides of the equation and then simplify.