Here are the solutions to each equation for the specified variable:

1. $g = 6x$, solve for $x$: $x = \frac{g}{6}$

2. $u = 2x - 2$, solve for $x$: $x = \frac{u + 2}{2}$

3. $z = m - x$, solve for $x$: $x = m - z$

4. $g = ca$, solve for $a$: $a = \frac{g}{c}$

5. $u = x - k$, solve for $x$: $x = u + k$

6. $g = c + x$, solve for $x$: $x = g - c$

7. $u = \frac{k}{a}$, solve for $a$: $a = \frac{k}{u}$

8. $g = xc$, solve for $x$: $x = \frac{g}{c}$

9. $12am = 4$, solve for $a$: $a = \frac{4}{12m} = \frac{1}{3m}$

10. $-3x + 2c = -3$, solve for $x$: $x = \frac{2c + 3}{3}$

11. $am = n + p$, solve for $a$: $a = \frac{n + p}{m}$

12. $u = \frac{ak}{b}$, solve for $a$: $a = \frac{ub}{k}$

13. $a - c = d - r$, solve for $a$: $a = d - r + c$

14. $xm = np$, solve for $x$: $x = \frac{np}{m}$

Would you like more detailed steps for any specific problem, or have further questions?

Related Questions

1. How would you solve each of these equations if the goal was a different variable?
2. What methods can be used to verify each solution?
3. How would these solutions change if additional terms or constraints were added?
4. What types of applications use equations similar to these?
5. How do inverse operations help in isolating variables in these equations?

Tip

When solving for a variable, identify operations in reverse order to systematically isolate it.