How do you solve 3/7x+1/2=3 by clearing the fractions?

3 Answers
Sep 30, 2017

x=35/6

Explanation:

3/7x+1/2=3

3/7x=3-1/2 isolate terms with variable
3/7x=\color(crimson)(6/2)-1/2 common denominator on right side
3/7x=5/2 simplify

3/7x(\color(teal)(2/2))=5/2(\color(teal)(7/7)) multiply to get common denominator overall
\color(seagreen)(6/14)x=\color(seagreen)(35/14)

x=\color(indigo)(35/14*14/6) divide (multiply by reciprocal for fractions) to get variable
x=35/6

Symbolab step-by-step

Sep 30, 2017

color(blue)(x=35/6 or color(blue)(5 5/6

Explanation:

3/7x+1/2=3

:.(6x+7)/14=42/14

multiply both sides by 14

:.6x+7=42

:.6x=42-7

:.6x=35

:.color(blue)(x=35/6 or color(blue)( 5 5/6

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check:-

:.3/7(color(blue)(35/6))+1/2=3

:.cancel3/cancel7^color(blue)1xxcancel35^color(blue)5/cancel6^color(blue)2+1/2=3

:.5/2+1/2=3

6/2=3

:.color(blue)(3=3

Sep 30, 2017

x =5 5/6

Explanation:

When you have an EQUATION with fractions, you can get rid of the denominators immediately by multiplying through by the LCM of the denominators to cancel them.

3/7x+1/2=3" "(LCD =color(blue)(14))

(color(blue)(14)xx3x)/7+(color(blue)(14)xx1)/2=color(blue)(14)xx3" "(larrxx color(blue)(14))

(color(blue)(cancel14^2)xx3x)/cancel7+(color(blue)(cancel14^7)xx1)/cancel2=color(blue)(14)xx3" "larr cancel denominators

6x+7 =42" "larr no fractions!

6x = 35

x = 35/6

x = 5 5/6