To solve the equation
\[ -10x + 13 + 12x = 5x - 8, \]
we want to manipulate it to get it into the form \(x = a\).
Let's analyze the given options:
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Subtract 10x from both sides of the equation and then simplify.
- This is a reasonable step because it allows us to combine the x terms.
- This would result in: \[ (12x - 10x) + 13 = 5x - 8 \implies 2x + 13 = 5x - 8. \]
-
Add 5x to both sides of the equation and then simplify.
- This step could also work but is not the simplest path; it leads to adding into both sides.
- If we do this, we would end up with: \[ -10x + 13 + 12x + 5x = -8 \implies 7x + 13 = -8. \]
-
Add 8 to both sides of the equation and then simplify.
- This could help isolate constants but doesn't directly lead to x.
- This would give us \( -10x + 13 + 12x + 8 = 0 \), and it's not effective for isolating x directly.
-
Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
- This is incorrect since adding terms should not result in 22x (should be combined correctly, producing 2x).
-
Subtract 13 from both sides of the equation and then simplify.
- This does help isolate x terms from constants. After performing this step, you will have all x terms on one side: \[ -10x + 12x = 5x - 8 - 13 \implies 2x = 5x - 21. \]
From the analysis, the two options that effectively transform the original equation into isolating \(x\) are:
- Subtract 10x from both sides of the equation and then simplify.
- Subtract 13 from both sides of the equation and then simplify.
So, the correct choices are:
- Subtract 10x from both sides of the equation and then simplify.
- Subtract 13 from both sides of the equation and then simplify.