2 Answers

x + 2  +  2x + 1

    5            3

Left side:  divide (x) and (2) by 5

x/5 = 1/5x

2/5  =  2/5

1/5x  +  2/5

Right side:  do the same as left side.

2/3x  +  1/3

Put problem together.

1/5x  +  2/5  =  2/3x  +  1/3  >  Make fractions denominator the same number.

3/15x  +  6/15  =  10/15x  +  5/15  >  cancel 3/15x on left by subtracting on both sides.

                                                               cancel 5/15 on right by subtracting on both sides.

3/15x - 3/15x  +  6/15 - 5/15  =  10/15x - 3/15x  +  5/15 - 1/15

                                       1/15   =    7/15x

Divide by 7/15 on both sides.

1/15 / 7/15   =   7/15x / 7/15

1/15 * 15/7  =  x

15/105  =  x   >  reduce

1/7  =  x

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I would have taken the short cut by looking at the denominators (5) and (3) and seeing the common denominator is 15. Then I will write the problem like this:

x + 2  +  2x + 1 

    5              3

Right side:  5 * 3 = 15  >  multiply the numerator by 3

3x  +  6

Left side:  3 * 5  = 15   >  multiply the numerator by 5

10x  +  5

Put problem together:

3x  +  6  =  10x  +  5

3x - 3x  +  6 - 5  =  10x - 3x  +  5 - 5

                       1     =      7x

                      7               7

x  =  1/7