To transform the equation \(-10x + 13 + 12x = 5x - 8\) into the form \(x = a\), we need to isolate \(x\). Let's examine the options provided:
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A) Add 5x to both sides of the equation and then simplify.
This will combine \(5x\) with the terms on the left side, leading us to isolate \(x\). This step is valid. -
B) Subtract 10x from both sides of the equation and then simplify.
This will help eliminate the \(-10x\) term on the left side. This step is also valid. -
C) Combine like terms 10x and 12x to get 22x, and then subtract 22x from both sides of the equation.
This step is incorrect because \(10x\) and \(12x\) cannot just be simply combined in the way described (since \(-10x + 12x\) simplifies to \(2x\), not \(22x\)). -
D) Subtract 13 from both sides of the equation and then simplify.
This will help in moving constant terms around and could eventually help isolate \(x\). This step is valid. -
E) Add 8 to both sides of the equation and then simplify.
This will help in isolating constants, and while it's a valid step towards simplification, it doesnβt directly help in isolating \(x\) immediately.
From the options evaluated, the correct ones to transform the equation into the form \(x = a\) and show that there is one solution are:
- A) Add 5x to both sides of the equation and then simplify.
- B) Subtract 10x from both sides of the equation and then simplify.
So, the final selected options are A and B.
1 answer