Question

Solve the equation if possible. $$ 9(b-4)-7 b=5(3 b-2) $$

Short answer

The solution to the equation is \(b = -2\).

Step-by-step solution

Distribute the Multiplication

Begin by distributing the multiplication through the parentheses in the equation: \(9b - 36 - 7b = 15b -10\).

Combine Like Terms on Each Side

Combine like terms on both sides of the equation, which will yield the simplified equation: \(2b - 36 = 15b - 10\)

Isolate the Variable

Attempt to isolate 'b' to one side of the equation. This can be done by subtracting \(2b\) from both sides and adding \(10\) to both sides, which gives you: \(-36 + 10 = 15b - 2b\).

Simplify

Now simplify again by combining like terms: \(-26 = 13b\).

Solve for the Variable

Lastly, solve for 'b' by dividing both sides of the equation by 13: \(-26/13 = b\) yields \(b = -2\).