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4 years ago

Solve the following equation for x: 6(4x+5)=3 (x+8)+3

2 answers:

5 0

Hello,

Shall we begin?

<span>6(4x+5)=3 (x+8)+3
</span>24x + 30 = 3x + 24 + 3
24x - 3x = 24 + 3 - 30
21x = - 3
x = -3 / 21
x = - 1/7

Answers: x = - 1/7

SCORPION-xisa [38]4 years ago

3 0

Hello,

Shall we begin?

6(4x+5)=3 (x+8)+3

24x + 30 = 3x + 24 + 3

24x - 3x = 24 + 3 - 30

21x = - 3

x = -3 / 21

x = - 1/7

Answers: x = - 1/7

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3 years ago

a ratio of north america butterflies to soulth american butteries at a butterflies at the park is 5:3. the ratio of south americ

dimaraw [331]

There are 18 south American butterflies in the park

<h3><u>Solution:</u></h3>

Given that , A ratio of north america butterflies to south american butteries at the park is 5 : 3

And the ratio of south american butterflies to eurpopean butterflies is 3:2.

There are 30 north american butterflies at the butterflies at the butterfly park

Number of north America butterflies : number of south American butterflies = 5 : 3

30 : number of south American butterflies = 5 : 3

[ since there are 30 north butterflies ]

$\frac{30}{\text { number of south american butterflies }}=\frac{5}{3}$

$30 \times 3=\text { number of south American butterflies } \times 5$

$\text { Number of south American butterflies } \times 5=90$

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3 years ago

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3 years ago

Y+1 y+8 y+2 y+7

kipiarov [429]

$\dfrac{y+1}{y+2}+\dfrac{y+8}{y+9}=\dfrac{y+2}{y+3}+\dfrac{y+7}{y+8}$

Write all fractions in terms of a common denominator:

$\dfrac{y+1}{y+2}=\dfrac{(y+1)(y+9)(y+3)(y+8)}{(y+2)(y+9)(y+3)(y+8)}$

$\dfrac{y+8}{y+9}=\dfrac{(y+8)^2(y+2)(y+3)}{(y+2)(y+9)(y+3)(y+8)}$

$\dfrac{y+2}{y+3}=\dfrac{(y+2)^2(y+9)(y+8)}{(y+2)(y+9)(y+3)(y+8)}$

$\dfrac{y+7}{y+8}=\dfrac{(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}$

Then move all fractions to one side and simplify the numerator:

$\dfrac{(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}=0$

The numerator dictates when the fraction reduces to 0. The denominator can never be 0, so we know that <em>y</em> cannot take any of the values -2, -9, -3, nor -8.

So the equation reduces to

$(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)=0$

Expand the left side; you would end up with

$-6(2y+11)=0$

$2y+11=0$

$2y=-11$

$\implies\boxed{y=-\dfrac{11}2}$

8 0

3 years ago