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Aleks [24]
2 years ago
8

WILL MARK B! Please I need help I have a quiz

Mathematics
2 answers:
Savatey [412]2 years ago
7 0

Answer:

a) [x:   -  \infty  < x  <  \infty ]

b)[x:  - 1]

c)  [x:-  \frac{5}{3} ]

d) [x: 3, 0]

e) [x:  -  \frac{1}{4} ]

MArishka [77]2 years ago
3 0

Answer:

a) 2x² - x + 3 = x(2x + 1) - 2x

<=> 2x² - x + 3 = 2x² + x - 2x

<=> 3 - x = - x

<=> 3 = 0

=> no solution

b) x/2 - x/3 - x/4 = 1/12

\frac{6x}{12}  -  \frac{4x}{12}  -  \frac{3x}{12}  =  \frac{1}{12}  \\  \\  \frac{ - x}{12}  =  \frac{1}{12}  \\  \\  =  >  - x = 1 \\  \\  \\  <  =  > x = 1

=> the euqation has the solution x = 1

c) |x - 5| = 2|x|

=> x - 5 = 2x

or x - 5 = -2x

<=> x = -5

or 3x = 5

<=> x = -5

x = -5or x = 5/3

d) defined conditions: 2 - x 》 0

<=> x 《 2

we have:

\sqrt{x + 4}  = 2 - x \\  <  =  > x + 4 = (2 - x) {}^{2}   \\  <  =  > x + 4 =  {x}^{2}  - 4x + 4 \\  <  =  >  {x}^{2}  - 5x = 0 \\  <  =  > x(x - 5) = 0 \\

<=> x = 0 (because x 《 2)

e)

\sqrt{5}  =  \frac{1}{25 {}^{x} }  \\   =  > 5 =  \frac{1}{25 {}^{2x} }  \\  <  =  > 5.25 {}^{2x}  = 1  \\ <  =  >  5.5 {}^{4x}  = 1 \\  <  =  > 5 {}^{4x + 1}  = 1 \\  =  > 4x + 1 = 0

<=> x = -1/4

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