Question

Solve the equation and describe each step you use. $$ -8 x+7=4 x-5 $$

Short answer

The solution to the equation \(-8x+7 = 4x-5\) is \(x = 1\).

Step-by-step solution

Rearrange the equation

To find the value of \(x\), you should begin by moving terms involving \(x\) to one side of the equation and the rest to the other side. You do this by adding \(8x\) to both sides and adding \(5\) to both sides of the equation: \(-8x + 8x + 7 + 5 = 4x + 8x - 5 + 5\). This simplifies to \(12 = 12x\)

Isolate Variable x

Now get \(x\) on its own by dividing both sides of the equation by \(12\): \(\frac{12}{12} = \frac{12x}{12}\). This gives the result: \(x = 1\).