I need to find the value of m in the following equation: (2m - 1)/3 = 5 + m/6I am doing a step wrong somewhere and when i reverse to check answer the value is incorrect. Could someone do it step...

I need to find the value of m in the following equation:

(2m - 1)/3 = 5 + m/6

I am doing a step wrong somewhere and when i reverse to check answer the value is incorrect. Could someone do it step by step so I can see where I'm going wrong? Thanks you!

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job518's profile pic

job518 | College Teacher | (Level 2) Adjunct Educator

Posted on

Be sure you have checked your parenthesis before continuing to ensure you have written the question correctly.

you could break it into separate fractions :

2/3 m -  1/3 = 5 + 1/6 m

get like terms together by subtracting 1/6 m from both sides

2/3 m - (1/6 m) - 1/3 = 5     ----> 1/6 m - 1/6 m =0

then add 1/3 to both sides

2/3 m - 1/6 m = 5 + 1/3   ---> -1/3 + 1/3 = 0

then find common denominators

4/6 m - 1/6 m = 15/3 + 1/3  --> 2/3 * 2/2 = 4/6  

                                            5/1 * 3/3 = 15/3

simplify

3/6 m = 16/3

multiply both sides by the reciprocal (flip it) of the coefficient (# in front of m)

6/3 * 3/6 m = 16/3 * 6/3

the fractions cancel each other out  on the left and the right yields 32/3

m = 32/3.

Plug it into original equation and check.

                                     

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

(2m-1)/3=5+m/6

Mutiply 6 both sides:

(2m-1)6/3= (5+m/6)6. simplify

2(2m-1)=30+m

4m-2=30+m.

Subtract m from both sides:

4m-2-m=30+m-m.simplify:

3m-2=30. Add 2 to both sides:

3m-2+2=30+2. simplify:

3m=32

Divide by 3 both sides:

m=32/3 = 10 and 2/3

 

Substite m=32/3 in original equation:

Left side:

{2*32/3)-1}/3 =  (64/3-1)/3=61/9.

Right side:5+(32/3)/6=5+16/9=(45+16)/9 =61/9.

So,LHS=RHS.

Hope this helps.

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