# How do you solve 4(5b +2)-b=2+8(3b-8)?

Jun 29, 2017

$b = 14$

#### Explanation:

Both brackets neednto be expanded first, where $a \left(b + c\right) \equiv a b + a c$

This means that $4 \left(5 b + 2\right) \equiv \left(4 \cdot 5 b\right) + \left(4 \cdot 2\right) = 20 b + 8$

It also means that $8 \left(3 b - 8\right) \equiv \left(8 \cdot 3 b\right) + \left(8 \cdot - 8\right) = 24 b - 64$

You now have $20 b + 8 - b = 2 + 24 b - 64$. Put all b's on the left hand side and numbers on the right.

$20 b + 8 - b = 2 + 24 b - 64$
$20 b - b - 24 b = - 8 + 2 - 64$
$- 5 b = - 70$

Now divide both sides by $- 5$.

$\frac{- 5 b}{- 5} = \frac{- 70}{- 5}$
$b = 14$

Jun 29, 2017

$b = 14$

#### Explanation:

$4 \left(5 b + 2\right) - b = 2 + 8 \left(3 b - 8\right)$

First open the brackets and simplify by multiplying each term with the number outside the bracket.

$20 b + 8 - b = 2 + 24 b - 64$

Simplify each side.

$19 b + 8 = 24 b - 62$

Add $62$ to each side.

$19 b + 70 = 24 b$

Subtract $19 b$ from each side.

$70 = 5 b$

Divide both sides by $5$.

$14 = b$