To determine how many solutions the equation \(7(20x + 5) = 16x - 2\) has, we can simplify and solve it step by step.
First, let's expand the left side of the equation: \[ 7(20x + 5) = 140x + 35 \] So, the equation becomes: \[ 140x + 35 = 16x - 2 \]
Next, we will move all terms involving \(x\) to one side and constant terms to the other side. We can subtract \(16x\) from both sides: \[ 140x - 16x + 35 = -2 \] This simplifies to: \[ 124x + 35 = -2 \]
Now, we will subtract \(35\) from both sides: \[ 124x = -2 - 35 \] This simplifies to: \[ 124x = -37 \]
Now, we divide both sides by \(124\): \[ x = -\frac{37}{124} \]
Since we found a specific value for \(x\), the equation has exactly one solution.
Thus, the answer is: A. 1