Question

1. how many solutions does the equation $3(4x + 1) = 6(2x - 5)$ have?

Explanation:

Step1: Expand both sides

First, we expand the left - hand side and the right - hand side of the equation using the distributive property \(a(b + c)=ab+ac\).
For the left - hand side: \(3(4x + 1)=3\times4x+3\times1 = 12x+3\)
For the right - hand side: \(6(2x - 5)=6\times2x-6\times5=12x - 30\)
So the equation becomes \(12x + 3=12x-30\)

Step2: Subtract \(12x\) from both sides

Subtract \(12x\) from both sides of the equation \(12x + 3=12x-30\).
\((12x + 3)-12x=(12x-30)-12x\)
Simplifying both sides: \(3=- 30\)

Answer:

The equation \(3(4x + 1)=6(2x - 5)\) has no solutions because after simplifying the equation, we get a contradiction (\(3=-30\)) which is never true for any value of \(x\).