Answer:
x = 24.
r [tex]$ \ne $[/tex] 0.
Step-by-step explanation:
2. The given equation is:
[tex]$ \frac{1}{2} (x - 4) = \frac{1}{3} x + 2 $[/tex]
a) To eliminate the fractions multiply the equation throughout by the LCM of the denominators of the fraction. In this case, the LCM of (2, 3). The LCM is 6. So, multiply the entire equation by 6.
b) Half of the difference between an integer and 4 equals the sum of one - third of the integer and 2. Find the integer.
c) We have the equation:
[tex]$ \frac{1}{2} (x - 4) = \frac{1}{3} x + 2 $[/tex]
Multiplying throughout by 6, we get:
[tex]$ \frac{6}{2}(x - 4) = \frac{6}{3} x + 6(2) $[/tex]
[tex]$ \implies 3(x - 4) = 2x + 12 $[/tex]
[tex]$ \implies 3x - 12 = 2x + 12 $[/tex]
[tex]$ \implies x = 24 $[/tex]
Therefore, the solution of the equation is 24.
3. The given equation is: [tex]$ ry + s = tx - m $[/tex]
To solve for y:
We can rearrange the equation as:
[tex]$ ry = tx - m - s $[/tex]
[tex]$ \implies y = \frac{tx - m - s}{r} $[/tex]
or, [tex]$ y = \frac{tx - (m + s)}{r} $[/tex]
Note that we have to impose a condition on variable [tex]$ r $[/tex]. It would be that [tex]$ r $[/tex] can never be zero. i.e., [tex]$ r \ne 0 $[/tex]. Otherwise, the value of [tex]$ y $[/tex] would be undefined.
