To solve the equation \(4.3(3.4x - 19.2) = 5.3x + 10.7 - 2.4x\), let's start simplifying the equation step by step.
First, simplify the right-hand side:
\[ 5.3x - 2.4x + 10.7 = (5.3 - 2.4)x + 10.7 = 2.9x + 10.7 \]
Now, the equation looks like this:
\[ 4.3(3.4x - 19.2) = 2.9x + 10.7 \]
Next, we can distribute \(4.3\) on the left side:
\[ 4.3 \cdot 3.4x - 4.3 \cdot 19.2 \]
That gives us:
\[ 14.62x - 82.56 = 2.9x + 10.7 \]
Now, we want to isolate \(x\).
Looking at the options provided to solve the equation, we can evaluate each one:
a. Add 10.7 to both sides of the equation.
- This is a valid step; it would help isolate \(x\).
b. Divide both sides of the equation by 3.4x.
- This is not a good step because it is not valid to divide by a variable; it could eliminate \(x\).
c. Subtract 2.9x from both sides of the equation.
- This is also a valid step; it would consolidate \(x\) terms on one side.
d. Multiply both sides of the equation by 10.7.
- This is not necessary and would complicate the equation further.
The best answers that are valid steps towards simplifying the equation are a and c. However, if I had to choose the best standard step to simplify the equations further, a would be a good choice to make the equation easier.
Therefore, the correct answer that describes a step that can be used to solve the equation for \(x\) is:
a. Add 10.7 to both sides of the equation.
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