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6x+4+11x/3+11x/3=360

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2 Answers

11x/3 is equivalent to (11/3)x.

Rewrite the terms like this and put all the terms together that have an x in them:

6x + (11/3)x + (11/3)x + 4 = 360

Add all the x terms together:

(6 + 11/3 + 11/3)(x) + 4 = 360

(40/3)(x) + 4 = 360

Subtract 4 from both sides:

(40/3)(x) = 356

Multiply both sides by (3/40), the reciprocal of the coefficient in front of the x:

(3/40)(40/3)(x) = (356)(3/40)

Simplify and you end up with:

x = 26.7

6x + 4 + 11x/3 + 11x/3 = 360

Unless you enjoy calculating fractions, I recommend you eliminate the fractions by multiplying by the greatest common factor (GCF).  In this case the GCF is 3, because it is the only denominator.  To keep the equation balanced while multiplying by the GCF, you need to multiply both sides of the equation by the GCF:

3(6x + 4 + 11x/3 + 11x/3) = 3(360)

To multiply the left side of the equation, use distributive property so each term is multiplied by 3:

3(6x) + 3(4) + 3(11x/3) + 3(11x/3) = 3(360)

When multiplying 3(11x/3), the GCF cancels out the denominator because 3/3 =1 so after multiplying each term you have:

18x + 12 + 11x + 11x = 1080

Combine like terms so you have:

40x + 12 = 1080

Now doing simple algebra:

40x + 12 = 1080

       -12         -12

     40x  =   1068

       40        40

          x  =  26  28/40  =  26  7/10 = 26.7