Solve Equation: 4x - 1/3 - 2x + 7/6 = 5/2

[Gringo123]

Have I solved this equation correctly? I don't think I have as I can't imagine the value of x being a recurring number.

4x - 1/3 - 2x + 7/6 = 5/2

I have worked it out as follows:

6(4x - 1) -3 (2x + 7) = 30/2
(here i have multiplied the right side by 6 as this is the LCM of 6 + 3.

24x - 6 - 6x - 21 = 15
18x - 27 = 15
18x = 42
x = 2.3333^r

 

[Mark44]

Have I solved this equation correctly? I don't think I have as I can't imagine the value of x being a recurring number.

4x - 1/3 - 2x + 7/6 = 5/2

From the work you show later, your original equation is not written correctly. Apparently this is what you have.
$$\frac{4x - 1}{3} - \frac{2x + 7}{3} = \frac{5}{2}$$

The way anyone who is at least halfway knowledgeable in mathematics would interpret your equation is this:
$$4x - \frac{1}{3} - 2x + \frac{7}{6} = \frac{5}{2}$$

If the first equation is what you meant and you don't know how to write it using LaTeX, use parentheses, like so:
(4x - 1)/3 - (2x + 7)/6 = 5/2

I have worked it out as follows:

6(4x - 1) -3 (2x + 7) = 30/2
(here i have multiplied the right side by 6 as this is the LCM of 6 + 3.

24x - 6 - 6x - 21 = 15
18x - 27 = 15
18x = 42
x = 2.3333^r