Question

solve the equation.

• 3(4p + 6) - 2(2 - 11p) = 2(8 + 3p)

p = \square

Explanation:

Step1: Distribute the coefficients

First, we distribute the -3, -2, and 2 across the parentheses:
$-3(4p + 6) = -12p - 18$
$-2(2 - 11p) = -4 + 22p$
$2(8 + 3p) = 16 + 6p$
So the equation becomes: $-12p - 18 - 4 + 22p = 16 + 6p$

Step2: Combine like terms

Combine the like terms on the left side:
$(-12p + 22p) + (-18 - 4) = 10p - 22$
So now the equation is: $10p - 22 = 16 + 6p$

Step3: Subtract 6p from both sides

Subtract 6p from both sides to get:
$10p - 6p - 22 = 16 + 6p - 6p$
$4p - 22 = 16$

Step4: Add 22 to both sides

Add 22 to both sides:
$4p - 22 + 22 = 16 + 22$
$4p = 38$

Step5: Divide by 4

Divide both sides by 4:
$p = \frac{38}{4} = \frac{19}{2} = 9.5$

Answer:

$p = \frac{19}{2}$ (or $p = 9.5$)