6x+7=5(4x-1)-16
To solve the equation \( 6x + 7 = 5(4x - 1) - 16 \), let's start by distributing and simplifying the right side:
Distribute the 5 on the right side: \[ 5(4x - 1) = 20x - 5 \]
Substitute this back into the equation: \[ 6x + 7 = 20x - 5 - 16 \]
Simplify the right side: \[ 20x - 5 - 16 = 20x - 21 \]
So the equation now looks like this: \[ 6x + 7 = 20x - 21 \]
Next, let's get all the \(x\) terms on one side and the constant terms on the other side. Subtract \(6x\) from both sides: \[ 7 = 20x - 6x - 21 \] This simplifies to: \[ 7 = 14x - 21 \]
Now, add 21 to both sides to isolate the term with \(x\): \[ 7 + 21 = 14x \] Thus, we have: \[ 28 = 14x \]
Finally, divide both sides by 14 to solve for \(x\): \[ x = \frac{28}{14} = 2 \]
So the solution is: \[ \boxed{2} \]
