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3 years ago

How to express each of the following pairs of

Mathematics

1 answer:

vichka [17]3 years ago

7 0

Answer:

a) 3<x<8

b) -4<x<-2

c) -6<x<5

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

e) 0<x<7

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;

-6<x<5

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;

-21/4 < x-8/3

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:

0<x<7

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Subtract 8/5 from both sides.

$\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4}{5}-\frac{8}{5} \ \ \end{gathered}$}$

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$\large\displaystyle\text{$\begin{gathered}\sf -\frac{8}{5}x=\frac{4-8}{5} \end{gathered}$}$

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Multiply both sides by $\bf{-\frac{5}{8}}$ , the reciprocal of $\bf{-\frac{5}{8}}$ .

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Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

$\large\displaystyle\text{$\begin{gathered}\sf x=\frac{-4(-5)}{5\times8} \ \to \ \ Multiply \end{gathered}$}$
$\large\displaystyle\text{$\begin{gathered}\sf x=\frac{20}{40} \end{gathered}$}$

Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.

$\boxed{\large\displaystyle\text{$\begin{gathered}\sf x=\frac{1}{2} \end{gathered}$}}$

Good luck in your studies

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Answer:

$a_1=1.04$

Step-by-step explanation:

We have a geometric sequence with:

$Sn = 89,800$ , $r = 3.4$ , and $n = 10$

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