Questions: Benchmark 1- Item 204972 Main 4x + 7 = 3x + 7 2(9x + 6) = 6x + 4 -3(2x - 5) = 15 - 6x 5x + 12 = 5x - 7 Which linear equation has no solution? CLEAR SUBMIT Language History Calculator NEXT >

Solution Steps

The first equation is: \[ 4x + 7 = 3x + 7 \] Subtract \(3x\) from both sides: \[ 4x - 3x + 7 = 7 \] Simplify: \[ x + 7 = 7 \] Subtract \(7\) from both sides: \[ x = 0 \] This equation has a unique solution: \(\boxed{x = 0}\).

The second equation is: \[ 2(9x + 6) = 6x + 4 \] Expand the left side: \[ 18x + 12 = 6x + 4 \] Subtract \(6x\) from both sides: \[ 12x + 12 = 4 \] Subtract \(12\) from both sides: \[ 12x = -8 \] Divide by \(12\): \[ x = -\frac{8}{12} = -\frac{2}{3} \] This equation has a unique solution: \(\boxed{x = -\frac{2}{3}}\).

The third equation is: \[ -3(2x - 5) = 15 - 6x \] Expand the left side: \[ -6x + 15 = 15 - 6x \] Add \(6x\) to both sides: \[ 15 = 15 \] This is always true, meaning the equation has infinitely many solutions. The solution is: \(\boxed{\text{All real numbers}}\).

Final Answer