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aalyn [17]
3 years ago
6

6.2÷(2x+1)=2 1/3 ÷4 find x

Mathematics
1 answer:
Norma-Jean [14]3 years ago
3 0

You can look at all the fractions and form the least common multiple of their denominators.

6.2 = 6 1/5 has a denominator of 5

÷ (2x+1) puts (2x+1) in the denominator

2 1/3 has a denominator of 3

÷ 4 puts 4 in the denominator

These denominators have no common factors, so the least common multiple of 5, (2x+1), 3, and 4 is their product: 60(2x+1). Multiply the equation by this value.

\dfrac{6.2}{(2x+1)}\times 60(2x+1)=\dfrac{2\frac{1}{3}}{4}\times 60(2x+1)\\\\372=35(2x+1)\\\\372=70x+35\qquad\text{eliminate parentheses}\\\\337=70x\qquad\text{subtract 35}\\\\x=\dfrac{337}{70}\qquad\text{divide by the x coefficient}

The solution is x = 337/70.

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How to solve this equation
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\bf \sqrt{5x+19}-4=3x-15
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3 years ago
I GIVE BRAINLIEST PLS HELP
ioda
The answer is 8
Here's why:
{ ( \frac{( {6}^{7}) \times ( {3}^{3})  }{(  {6}^{6}) \times ( {3}^{4}  ) } )}^{3}  =   \\ ( \frac{6}{3} ) ^{3}  =  \\ \frac{216}{27}  = 8
The exponents are subtracted one from another when divided.
\frac{ a ^{b} }{ {a}^{c} } =  {a}^{b - c}
We can look at the problem this way:
( \frac{6^{7} }{6 ^{6} }  \times  \frac{3^{3} }{ {3}^{4} } ) = (6^{7 - 6}  \times  {3}^{3 - 4} ) =  \\ ({6}^{1}  \times  {3}^{ - 1} )
Since we have the power of -1 on the 3, we apply this rule:
{a}^{ - b}  =  \frac{1}{ {a}^{b} }
Also this rule because we have the power of 1 on the 6:
{a}^{1}  = a
Then we get this:
(6 \times  \frac{1}{3} )^{3}  = ( \frac{6}{3} )^{3}
We apply the rule:
( \frac{a}{b}) ^{c}   =  \frac{ {a}^{c} }{ {b}^{c} }
We get this:
\frac{{6}^{3} }{ {3}^{3} } =  \frac{216}{27}  = 8
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