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Solve the following equations: 2x-2=3x...

Solve the following equations:
`2x-2=3x+7`

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To solve the equation \(2x - 2 = 3x + 7\), follow these steps: ### Step 1: Rearrange the equation We want to get all the terms involving \(x\) on one side and the constant terms on the other side. We can start by subtracting \(3x\) from both sides. \[ 2x - 2 - 3x = 3x + 7 - 3x \] This simplifies to: \[ 2x - 3x - 2 = 7 \] ### Step 2: Combine like terms Now, combine the \(x\) terms on the left side: \[ -1x - 2 = 7 \] ### Step 3: Isolate the \(x\) term Next, we want to isolate the term with \(x\). To do this, we will add \(2\) to both sides of the equation: \[ -1x - 2 + 2 = 7 + 2 \] This simplifies to: \[ -1x = 9 \] ### Step 4: Solve for \(x\) Now, to solve for \(x\), we can multiply both sides by \(-1\): \[ x = -9 \] ### Final Answer The solution to the equation \(2x - 2 = 3x + 7\) is: \[ x = -9 \] ---
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