Question 1

What is the solution-2|2.2x-3.3|=-6.6

Question 2

Answer:

-2(-3.3 + 2.2x) = 6.6

(-3.3 * -2 + 2.2x * -2) = 6.6

(6.6 + -4.4x) = 6.6

Question 3

$Solution, solve\:for\:x,\:-2\left|2.2x-3.3\right|=-6.6\quad :\quad x=0\quad \mathrm{or}\quad \:x=3$

Steps:

$-2\left|2.2x-3.3\right|=-6.6$

$\mathrm{Divide\:both\:sides\:by\:}-2,\\(-2\left|2.2x-3.3\right|)/(-2)=(-6.6)/(-2)$

$\mathrm{Simplify},\\\left|2.2x-3.3\right|=3.3$

$|f\left(x\right)|=a\quad \Rightarrow \:f\left(x\right)=-a\quad \mathrm{or}\quad \:f\left(x\right)=a,\\2.2x-3.3=-3.3\quad \quad \mathrm{or}\quad \:\quad \:2.2x-3.3=3.3$

$2.2x-3.3=-3.3,\\\mathrm{Add\:}3.3\mathrm{\:to\:both\:sides},\\2.2x-3.3+3.3=-3.3+3.3,\\\mathrm{Refine},\\2.2x=0,\\\mathrm{Multiply\:both\:sides\:by\:}10,\\.2x\cdot \:10=0\cdot \:10,\\\mathrm{Refine},\\22x=0,\\\mathrm{Divide\:both\:sides\:by\:}22,\\(22x)/(22)=(0)/(22),\\\mathrm{Simplify},\\x=0$

$2.2x-3.3=3.3,\\\mathrm{Multiply\:both\:sides\:by\:}10,\\2.2x\cdot \:10-3.3\cdot \:10=3.3\cdot \:10,\\\mathrm{Refine},\\22x-33=33,\\\mathrm{Add\:}33\mathrm{\:to\:both\:sides},\\22x-33+33=33+33,\\\mathrm{Simplify},\\22x=66,\\\mathrm{Divide\:both\:sides\:by\:}22,\\(22x)/(22)=(66)/(22),\\\mathrm{Simplify},\\x=3$