Ask AI: what is the solution for -4\left(2m-7\right)=3\left(52-4m\right)

To solve the equation \(-4(2m-7)=3(52-4m)\), follow these steps: 1. Distribute the constants on each side of the equation: \[ -4(2m - 7) = 3(52 - 4m) \] \[ -4 \cdot 2m + (-4) \cdot (-7) = 3 \cdot 52 + 3 \cdot (-4m) \] \[ -8m + 28 = 156 - 12m \] 2. Move all terms involving \(m\) to one side and constant terms to the other side. Let's move \(-12m\) to the left side by adding \(12m\) to both sides. Similarly, let's move \(28\) to the right side by subtracting \(28\) from both sides: \[ -8m + 12m = 156 - 28 \] \[ 4m = 128 \] 3. Finally, solve for \(m\) by dividing both sides by 4: \[ m = \frac{128}{4} \] \[ m = 32 \] So, the solution to the equation is \(m = 32\).