(x+2)/3 = (2x+1)/2 - Please help, maths question

HELP!!! could you do it in steps? find x ;
x+2/3 = 2x+1/2

Find a number that all the denominators go into (2 and 3 both go into 6) so multiply everything by 6:

6(x+2)/3 = 6(2x+1)/2

Now simplify the fractions:

2(x+2) = 3(2x+1)

Expand the brackets:

2x + 4 = 6x + 3

Subtract 4 from both sides:

2x = 6x - 1

Subtract 6x from both sides:

-4x = -1

Divide both sides by -4:

x = 1/4

(x+2)/3 = (2x+1)/2

here you can multiply through by 6 to get rid of the fractions
[always get rid of the fractions]
when you get into more interesting equations, you will have binomials for denominators

so
multiply through by 3
(x+2) = 3(2x+1)/2

multiply through by 2
2(x+2) = 3(2x+1)

distribute into the parentheses
(2x+4)=(6x+3)

1=4x
x=1/4

(x+2)/3 = (2x+1)/2

Find the Least Common Denominator (LCD) which is 6.

2(x+2)/6 = 3(2x+1)/6
2(x+2) = 3(2x+1)
2x+4 = 6x+3
4-3=6x-2x
1=4x

x=1/4 or 0.25

Test:
(0.25+2)/3 = (2[0.25]+1)/2
2.25/3 = 1.5/2
0.75 = 0.75

x is confirmed (=) 0.25.

Cross-multiply.

3(2x + 1) = 2(x + 2)

6x + 3 = 2x + 4

4x + 3 = 4

4x = 1

x = 0.25

I hope this information was very helpful.

(x+2)/3 = (2x+1)/2
2(x+2) = (2x+1)3
2x+4 = 6x+3
4-3 = 6x-2x
1 = 4x
x = 1/4

(x+2)/3 = (2x+1)/2
6[(x+2)/3 = (2x+1)/2]
2(x + 2) = 3(2x + 1)
2x + 4 = 6x + 3
1 = 4x
x = 1/4

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