Question

6.2÷(2x+1)=2 1/3 ÷4 find x

Answer 1

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.