# How do you solve 3(p-2)+7=32-4(2p+5)?

Jul 6, 2016

$p = 1$

#### Explanation:

To solve $3 \left(p - 2\right) + 7 = 32 - 4 \left(2 p + 5\right)$

Begin by distributing the values outside the parenthesis to the terms inside the parenthesis

$3 p - 6 + 7 = 32 - 8 p - 20$

Combine like terms on each side of the equation

$3 p - 6 + 7 = 32 - 8 p - 20$

$3 p + 1 = 12 - 8 p$

Now combine the variable terms on the same side of the equation by additive inverse

$3 p + 8 p + 1 = 12 \cancel{- 8 p} \cancel{+ 8 p}$

$11 p + 1 = 12$

Now combine constant terms on the same side of the equation by additive inverse

$11 p \cancel{+ 1} \cancel{- 1} = 12 - 1$

$11 p = 11$

Now solve for the variable by multiplicative inverse

$\frac{\cancel{11} p}{\cancel{11}} = \frac{11}{11}$

$p = 1$