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?: -10x + 13 + 12x = 5x - 8

Question

A. Subtract 10x from both sides of the equation and then simplify.
B. Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
C. Add 5x to both sides of the equation and then simplify.
D. Subtract 13 from both sides of the equation and then simplify.
E. Add 8 to both sides of the equation and then simplify.

Answer 1

To transform the equation \(-10x + 13 + 12x = 5x - 8\) into the form \(x = a\), we need to simplify and combine like terms properly.

Let's analyze the provided options:

Option A: Subtract \(10x\) from both sides of the equation and then simplify.
This would give us:
\(-10x + 12x + 13 = 5x - 10x - 8\)
\(2x + 13 = -5x - 8\), which can complicate the process.

Option B: Combine like terms \(10x\) and \(12x\) to get \(22x\), and then subtract \(22x\) from both sides of the equation.
This step is incorrect since there is no \(10x\) on the left side of the equation.

Option C: Add \(5x\) to both sides of the equation and then simplify.
This would give us:
\(-10x + 12x + 5x + 13 = -8\)
Which simplifies incorrectly since it would not lead directly to a solvable form.

Option D: Subtract \(13\) from both sides of the equation and then simplify.
This would give:
\(-10x + 12x = 5x - 8 - 13\)
or
\(2x = 5x - 21\). This might lead to simplifying further, but not directly toward \(x = a\).

Option E: Add \(8\) to both sides of the equation and then simplify.
This gives us:
\(-10x + 13 + 12x + 8 = 5x\)
or
\(2x + 21 = 5x\).

So among all these options, none seem to directly lead toward the simplest \(x = a\) format with one clear solution.

However, let’s start by simplifying our original equation step-by-step to determine which transformations yield the one solution:

The initial equation is:
\(-10x + 12x + 13 = 5x - 8\)

Combining \( -10x\) and \(12x\), we have:
\(2x + 13 = 5x - 8\).

Subtract \(5x\) from both sides:
\(2x - 5x + 13 = -8\)
which simplifies to:
\(-3x + 13 = -8\)

Then, subtract \(13\) from both sides:
\(-3x = -8 - 13\)
\(-3x = -21\)

Finally, divide both sides by \(-3\):
\(x = 7\).

This verifies that combining like terms was indeed essential and understood clearly.

Given that closer analysis reveals every path leads to the same, as none of the given are strictly leading to the end transformation straight as \(x = a\), I still suggest:

Ultimately, unless additional steps becoming precise as required do line up from it, Option A would have yielded progress towards arriving at one solution accurately but would lead more intricate results than needed. Thus, starting from there allows a clearer progression.

In essence—no singularly clear option suffices as always valid but consider Boxed selections as more pruning methods.

Answer 2

but which ones are correct

Answer 3

Let's clarify the options and determine which are correct in transforming the equation \(-10x + 13 + 12x = 5x - 8\) into a form \(x = a\).

We start with the equation: \[ -10x + 13 + 12x = 5x - 8 \]

Now, let's analyze the options one by one to see if they lead us to the form \(x = a\):

Option A: Subtract \(10x\) from both sides of the equation and then simplify.
\[ -10x + 12x + 13 = 5x - 8
\Rightarrow 2x + 13 = 5x - 8
\Rightarrow 13 = 5x - 2x - 8 \quad (continue solving) \] This will lead to a correct solution, so Option A is a valid step.

Option B: Combine like terms \(10x\) and \(12x\) to get \(22x\), and then subtract \(22x\) from both sides of the equation.
This is incorrect because there is no \(10x\) term on the left side to combine with \(12x\). Therefore, Option B is not valid.

Option C: Add \(5x\) to both sides of the equation and then simplify.
\[ -10x + 12x + 5x + 13 = -8
\Rightarrow 7x + 13 = -8 \quad (continue solving) \] This leads toward a solution, so Option C is valid.

Option D: Subtract \(13\) from both sides of the equation and then simplify.
\[ -10x + 12x = 5x - 8 - 13
\Rightarrow 2x = 5x - 21 \quad (continue solving) \] This is a valid transformation resulting in a solvable equation, so Option D is also valid.

Option E: Add \(8\) to both sides of the equation and then simplify.
\[ -10x + 12x + 13 + 8 = 5x
\Rightarrow 2x + 21 = 5x \quad (continue solving) \] This transformation also leads to a solvable equation, thus Option E is valid.

To summarize, the correct options for transforming the equation into the form \(x = a\) are:

• Option A
• Option C
• Option D
• Option E

Option B is not a valid step.