1) \( 5(x-3)=-2(x-4)+6 \)

To solve the equation \( 5(x-3)=-2(x-4)+6 \), let's first simplify both sides. Distributing on the left gives us \( 5x - 15 \). On the right, distribute the \(-2\) to get \(-2x + 8 + 6\), which simplifies to \(-2x + 14\). Now the equation looks like this: \[ 5x - 15 = -2x + 14 \] Next, let's add \(2x\) to both sides: \[ 5x + 2x - 15 = 14 \] This simplifies to: \[ 7x - 15 = 14 \] Adding 15 to both sides results in: \[ 7x = 29 \] Finally, divide by 7: \[ x = \frac{29}{7} \] So the solution to the equation is \( x = \frac{29}{7} \). Now you can plug this value back into the original equation to check your work!