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

1. Solve \(2x-5=3\): - Add \(5\) to both sides: \[ 2x = 3 + 5 = 8 \] - Divide both sides by \(2\): \[ x = \frac{8}{2} = 4 \] 2. Solve \(4x+6=x-3\): - Subtract \(x\) from both sides: \[ 3x + 6 = -3 \] - Subtract \(6\) from both sides: \[ 3x = -3 - 6 = -9 \] - Divide both sides by \(3\): \[ x = \frac{-9}{3} = -3 \] 3. Solve \(5a-3(a+1)=2-3a\): - Distribute the \(-3\) on the left: \[ 5a - 3a - 3 = 2 - 3a \] - Combine like terms on the left: \[ 2a - 3 = 2 - 3a \] - Add \(3a\) to both sides: \[ 2a + 3a - 3 = 2 \quad \Rightarrow \quad 5a - 3 = 2 \] - Add \(3\) to both sides: \[ 5a = 2 + 3 = 5 \] - Divide both sides by \(5\): \[ a = \frac{5}{5} = 1 \] 4. Solve \(2(x+2)=6(x+1)-(x-4)\): - Expand both sides: - Left-hand side: \[ 2(x+2)= 2x+4 \] - Right-hand side: \[ 6(x+1)-(x-4)=6x+6-x+4 = 5x+10 \] - Set the equation: \[ 2x+4 = 5x+10 \] - Subtract \(2x\) from both sides: \[ 4 = 3x+10 \] - Subtract \(10\) from both sides: \[ -6 = 3x \] - Divide both sides by \(3\): \[ x = \frac{-6}{3} = -2 \]