To solve the equation, let's start by translating the given statement into a mathematical equation:
The sum of [tex]\(-2m\)[/tex] and [tex]\(3m\)[/tex] is equal to the difference of [tex]\(\frac{1}{2}\)[/tex] and [tex]\(\frac{1}{3}\)[/tex].
So, we can write it as:
[tex]\[ -2m + 3m = \frac{1}{2} - \frac{1}{3} \][/tex]
Next, let's simplify the left side of the equation:
[tex]\[ -2m + 3m = (3m - 2m) = m \][/tex]
Now our equation is:
[tex]\[ m = \frac{1}{2} - \frac{1}{3} \][/tex]
To solve for [tex]\(m\)[/tex], we need to calculate the right side of the equation. To do this, we should first convert the fractions to a common denominator. The denominators are 2 and 3, so the least common denominator is 6.
Convert [tex]\(\frac{1}{2}\)[/tex] to the common denominator of 6:
[tex]\[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \][/tex]
Convert [tex]\(\frac{1}{3}\)[/tex] to the common denominator of 6:
[tex]\[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \][/tex]
Now we can subtract these fractions:
[tex]\[ \frac{1}{2} - \frac{1}{3} = \frac{3}{6} - \frac{2}{6} = \frac{3 - 2}{6} = \frac{1}{6} \][/tex]
So, we have:
[tex]\[ m = \frac{1}{6} \][/tex]
Therefore, the solution to the equation is:
[tex]\[ m = 0.16666666666666666 \][/tex]
