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Alexandra [31]
3 years ago
14

How to express each of the following pairs of

Mathematics
1 answer:
vichka [17]3 years ago
7 0

Answer:

<em>a) 3<x<8</em>

<em>b) -4<x<-2</em>

<em>c) -6<x<5</em>

<em>d) -21/4 < x-8/3</em>

<em>e) 0<x<7</em>

Step-by-step explanation:

Given the following inequalities

a)  x > 3, 2x - 3 < 15

Solve 2x - 3 < 15

2x < 15+3

2x<18

x<18/2

x<8

Combine x>3 and x<8

If x>3, then 3<x

On combining, we have:

3<x<8

b) For the inequalities 25 > 1 - 6x, 1 > 3x + 7

25 > 1 - 6x

25-1>-6x

24>-6x

Divide through by -6:

24/-6 > -6x/-6

-4 <x

For the inequality 1 > 3x + 7

1-7>3x

-6>3x

-6/3 > 3x/3

-2 > x

x < -2

Combining both results i.e -4 <x and x < -2, we will have:

-4<x<-2

c) For the inequalities 2x - 7<3< 27 + 4x

On splitting:

2x - 7<3 and 3< 27 + 4x

2x < 3+7

2x<10

x<5

Also for 3< 27 + 4x

3-27<4x

-24<4x

-24/4 < 4x/4

-6<x

Combining both solutions i.e x<5 and -6<x will give;

<em>-6<x<5</em>

d) For the inequalities 3x + 8 <0 < 21 + 4x

3x + 8 <0

3x < -8

x < -8/3

Also for 0 < 21 + 4x

0-21<4x

-21<4x

-21/4 < 4x/4

-21/4 < x

Combining -21/4 < x and x < -8/3 will give;

<em>-21/4 < x-8/3</em>

<em></em>

e) For the inequalities 5x - 36 < -1 < 2x – 1​

Split:

5x - 36 < -1

5x < -1+36

5x<35

5x/5 < 35/5

x < 7

For the expression -1 < 2x – 1​

-1+1 < 2x

0 < 2x

0<x

Combining both inequalities 0<x and x < 7 will give:

<em>0<x<7</em>

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Simplify LaTeX: \Large\frac{-4^{6} \cdot 4^{2}}{4^{4}}
Oksanka [162]

⇨ The value of this <u>simplified expression</u> = -4096/1 or -4096.

<h3>   </h3>
  • To solve this expression, just multiply the power base by how many times indicate the exponent, and then divide the numerator and denominator of the fraction by the same number.

Power or potentiation is a multiplication in equal factors, where there are <em>terms responsible</em> for obtaining the final result. An potency is given by \large \sf a^{n}. The terms of a power are:

<h3>     </h3>
  • Base
  • Exponent
  • equal factors
  • power
<h3>         </h3>

✏️ <u>Resolution/Answer</u>:

\\ \large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=\\\\

  • Multiply the powers of the numbers at numerator of the fraction, with the base <em>being multiplied by how many times</em> to indicate the exponent.

\\\large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-4\cdot4\cdot4\cdot4\cdot4\cdot4\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-4\cdot4\cdot4\cdot4\cdot16\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-4\cdot4\cdot16\cdot16\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 4^{2}}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 4\cdot4}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4^{4}}=\\\\

  • <em>Multiply </em>the power at denominator of the fraction:

\\\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4^{4}}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{4\cdot4}=

\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{16}=\\\\

  • <em>Multiply </em>the numerator numbers together:

\\\large \sf \dfrac{-16\cdot16\cdot16\cdot 16}{16}=

\large \sf \dfrac{-16\cdot16\cdot 256     }{16}=

\large \sf \dfrac{-256\cdot 256     }{16}=

\large \sf \dfrac{- 65536  }{16}=\\\\

  • Simplify the fraction by number 16:

\\\large \sf \dfrac{- 65536  }{16}=

\large \sf \dfrac{- 65536  \div16}{16\div16}=

{\orange{\boxed{\boxed{\pink {\large \displaystyle \sf { \frac{-4096}{1}  \ or \ -4096 }}}}}} \\\\\\

  • So this expression in its simplified form = -4096/1 or -4096.

{\orange{\boxed{\boxed{\pink {\large \displaystyle \sf { \frac{-4096}{1}  \ or \ -4096 }}}}}}\\\\

                                 ★ Hope this helps! ❤️

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