Questions: -3x+1=5x-7

-3x+1=5x-7
Transcript text: 3. $-3 x+1=5 x-7$
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Solution

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Solution Steps

To solve the equation \(-3x + 1 = 5x - 7\), we need to isolate the variable \(x\). This involves moving all terms containing \(x\) to one side of the equation and the constant terms to the other side. Then, we can solve for \(x\).

Step 1: Rearranging the Equation

We start with the equation: \[ -3x + 1 = 5x - 7 \] To isolate \(x\), we first move all terms involving \(x\) to one side and constant terms to the other side. This gives us: \[ 1 + 7 = 5x + 3x \]

Step 2: Simplifying the Equation

Now, we simplify both sides: \[ 8 = 8x \]

Step 3: Solving for \(x\)

Next, we divide both sides by 8 to solve for \(x\): \[ x = 1 \]

Final Answer

The solution to the equation is \(\boxed{x = 1}\).

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