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3 years ago

Solve for X. -3/2(x-2)=45/14 Please show work.

Mathematics

2 answers:

ICE Princess25 [194]3 years ago

7 0

Answer:

-1/7

Step-by-step explanation:

-3/2(x-2)=45/14

x-2=(45/14)/(-3/2)

x-2=(45/14)(-2/3)

x-2=-90/42

simplify -90/42 into -15/7

x-2=-15/7

x=-15/7+2

x=-15/7+14/7

x=-1/7

Y_Kistochka [10]3 years ago

6 0

Exact Form:
x=-1/7

Decimal form:

-0.142857

Explanation:
You simplify both sides of the equation and then isolate the variable.

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Read 2 more answers

Is the sum of an irrational number and rational number always irrational?

MissTica

Yes.

It can be proved by contradiction.

Let:
a - a rational number
b - an irrational number
c - the sum of a and b

$a+b=c$

Let assume that c is a rational number. Then a and c can be expressed as fractions with integer numerator and denominator:
$a=\dfrac{d}{e}\\
c=\dfrac{f}{g}\\$ where $d,e,f,g \in \mathbb{Z}$

$\dfrac{d}{e}+b=\dfrac{f}{g}\\
b=\dfrac{f}{g}-\dfrac{d}{e}\\
b=\dfrac{ef}{eg}-\dfrac{dg}{eg}\\
b=\dfrac{ef-dg}{eg}$

Since $d,e,f,g$ are all integers, then the products $ef,dg,eg$ and the difference $ef-dg$ are integers as well. It means that the number $b$ is a rational number, but this on the other hand contradicts the earlier assumption that $b$ is an irrational number. Therefore $c$ must be an irrational number.

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