How do you solve (2(2b+1))/3=3(b-2)?

1 Answer
Jan 10, 2018

b=4

Explanation:

\frac{2(2b+1)}{3}=3(b-2)

Let's remove the denominator from the left multiplying both side with the same quantity, in this case 3 so we can simplify
\color(blue)\cancel{3}*\frac{2(2b+1)}{\cancel{3}}=3(b-2)\color(blue){*3}

2(2b+1)=9(b-2)

Now let's do the multiplication
4b+2=9b-18

And move all the terms with b to the left and all the constants (terms without letter) to the right. Every time we move something to the other side let's change the sign.

4b-9b=-2-18
-5b = -20

Multiply with -1 to get a positive b
\color(blue){(-1)}-5b = -20 \color(blue){(-1)}
5b=20

\frac{\cancel{5}}{\cancel{5}}b=\frac{20}{5}
b=4