1. **State the problem:** Solve the equation $$10 - 6v = -104$$ for $v$. 2. **Isolate the variable term:** Subtract 10 from both sides: $$10 - 6v - 10 = -104 - 10$$ $$\cancel{10} - 6v - \cancel{10} = -104 - 10$$ $$-6v = -114$$ 3. **Solve for $v$:** Divide both sides by $-6$: $$\frac{-6v}{-6} = \frac{-114}{-6}$$ $$\cancel{-6}v/\cancel{-6} = 19$$ $$v = 19$$ --- 1. **State the problem:** Solve the equation $$-9x - 13 = -103$$ for $x$. 2. **Isolate the variable term:** Add 13 to both sides: $$-9x - 13 + 13 = -103 + 13$$ $$-9x = -90$$ 3. **Solve for $x$:** Divide both sides by $-9$: $$\frac{-9x}{-9} = \frac{-90}{-9}$$ $$x = 10$$ --- 1. **State the problem:** Solve the equation $$-10 = -10 + 7m$$ for $m$. 2. **Isolate the variable term:** Add 10 to both sides: $$-10 + 10 = -10 + 7m + 10$$ $$0 = 7m$$ 3. **Solve for $m$:** Divide both sides by 7: $$\frac{0}{7} = \frac{7m}{7}$$ $$0 = m$$ --- 1. **State the problem:** Solve the equation $$\frac{m}{9} - 1 = -2$$ for $m$. 2. **Isolate the fraction:** Add 1 to both sides: $$\frac{m}{9} - 1 + 1 = -2 + 1$$ $$\frac{m}{9} = -1$$ 3. **Solve for $m$:** Multiply both sides by 9: $$9 \times \frac{m}{9} = 9 \times (-1)$$ $$\cancel{9} \times \frac{m}{\cancel{9}} = -9$$ $$m = -9$$ --- 1. **State the problem:** Solve the equation $$7(9 + k) = 84$$ for $k$. 2. **Expand the left side:** $$7 \times 9 + 7 \times k = 84$$ $$63 + 7k = 84$$ 3. **Isolate the variable term:** Subtract 63 from both sides: $$63 + 7k - 63 = 84 - 63$$ $$7k = 21$$ 4. **Solve for $k$:** Divide both sides by 7: $$\frac{7k}{7} = \frac{21}{7}$$ $$k = 3$$ --- 1. **State the problem:** Solve the equation $$-243 = -9(10 + x)$$ for $x$. 2. **Divide both sides by $-9$ to isolate the parentheses:** $$\frac{-243}{-9} = \frac{-9(10 + x)}{-9}$$ $$27 = 10 + x$$ 3. **Isolate $x$:** Subtract 10 from both sides: $$27 - 10 = 10 + x - 10$$ $$17 = x$$ --- **Final answers:** - $v = 19$ - $x = 10$ - $m = 0$ - $m = -9$ - $k = 3$ - $x = 17$