1. \( 6 x+7=7 x+13 \)

To solve the equation \( 6x + 7 = 7x + 13 \) for \( x \), follow these steps: ### Step 1: Write Down the Equation \[ 6x + 7 = 7x + 13 \] ### Step 2: Gather Like Terms First, we want to get all the terms containing \( x \) on one side and the constant terms on the other side. - **Subtract \( 6x \) from both sides** to eliminate \( x \) from the left side: \[ 6x + 7 - 6x = 7x + 13 - 6x \] Simplifies to: \[ 7 = x + 13 \] ### Step 3: Isolate the Variable \( x \) - **Subtract 13 from both sides** to solve for \( x \): \[ 7 - 13 = x + 13 - 13 \] Simplifies to: \[ -6 = x \] ### Step 4: Write the Solution \[ x = -6 \] ### Verification To ensure that \( x = -6 \) is the correct solution, substitute it back into the original equation: \[ 6(-6) + 7 = 7(-6) + 13 \] \[ -36 + 7 = -42 + 13 \] \[ -29 = -29 \] Since both sides of the equation are equal, \( x = -6 \) is indeed the correct solution. **Answer:** \( x = -6 \)