A number k is less than 3 units from 10. What's the absolute value inequality???

Mathematics

1 answer:

Brrunno [24]3 years ago

6 0

It would be: k+3 = 10

subtracting 3 from both sides,

k+3-3 = 10-3

k=7

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3 years ago

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

mylen [45]

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

$Steps:$

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

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

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

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

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

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