Question

lesson 2.5 review - solving rational equations
①
\\(\frac{x}{(x + 1)} + \frac{3x + 4}{(x + 1)} = \frac{3}{1}\frac{(x + 1)}{(x + 1)}\\)
\\(x + 3x + 4 = 3(x + 1)\\)
\\(4x + 4 = 3x + 3\\)
① factor, lcm (lco)
multiple-choice question
what would you do on both sides to try to isolate x?
add 3x on both sides. then subtract the 4 from both sides.
that should result in \\(x = -1\\) as the solution.
subtract 3x on both sides. then subtract the 4 from both sides.
that should result in \\(x = -1\\) as the solution.
subtract 3x on both sides. then add 4 to both sides.
that should result in \\(x = -1\\) as the solution.
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Explanation:

Step1: Analyze the equation

We have the equation \(4x + 4=3x + 3\) after simplifying the rational equation.

Step2: Isolate \(x\)

First, we want to get rid of the \(3x\) on the right side. So we subtract \(3x\) from both sides:
\(4x+4 - 3x=3x + 3-3x\)
Which simplifies to \(x + 4=3\)
Then, we want to get rid of the \(4\) on the left side. So we subtract \(4\) from both sides:
\(x+4 - 4=3 - 4\)
Which gives \(x=- 1\)
Now let's check the options:

• Option 1: Adding \(3x\) would not help in isolating \(x\) as it would make the equation more complicated. So this is wrong.
• Option 2: Subtracting \(3x\) from both sides (as we did in step 2) and then subtracting \(4\) from both sides gives us the solution \(x =- 1\). This matches our steps.
• Option 3: After subtracting \(3x\), we should subtract \(4\) (not add \(4\)) to isolate \(x\). So this is wrong.

Answer:

The correct option is: Subtract 3x on both sides. Then subtract the 4 from both sides.
That should result in \(x=-1\) as the solution.