Literal Equations: Examples and Solutions

📚 Quick Study Guide

• 🔍 Definition: A literal equation is an equation where variables represent known values. We rearrange these equations to solve for a specific variable.
• 🔢 Basic Steps:
  • Isolate the term containing the variable you want to solve for.
  • Use inverse operations (addition, subtraction, multiplication, division) to get the variable by itself.
• ➕ Addition/Subtraction Property: You can add or subtract the same value from both sides of the equation without changing its solution.
• ✖️ Multiplication/Division Property: You can multiply or divide both sides of the equation by the same non-zero value without changing its solution.
• 💡 Example: Solve for $x$ in the equation $ax + b = c$. 1. Subtract $b$ from both sides: $ax = c - b$. 2. Divide both sides by $a$: $x = \frac{c-b}{a}$.

🧪 Practice Quiz

1. Solve for $x$ in the equation $y = mx + b$.

   1. $x = y - mx - b$
   2. $x = \frac{y - b}{m}$
   3. $x = \frac{y + b}{m}$
   4. $x = my + b$

2. Solve for $r$ in the equation $A = \pi r^2$.

   1. $r = \frac{A}{\pi}$
   2. $r = \sqrt{\frac{A}{\pi}}$
   3. $r = A - \pi$
   4. $r = \frac{\sqrt{A}}{\pi}$

3. Solve for $h$ in the equation $V = \frac{1}{3}Bh$.

   1. $h = \frac{V}{3B}$
   2. $h = \frac{3V}{B}$
   3. $h = 3V - B$
   4. $h = \frac{B}{3V}$

4. Solve for $w$ in the equation $P = 2l + 2w$.

   1. $w = \frac{P - 2l}{2}$
   2. $w = \frac{P}{2l + 2}$
   3. $w = \frac{P}{2} - l$
   4. $w = P - l$

5. Solve for $C$ in the equation $F = \frac{9}{5}C + 32$.

   1. $C = \frac{5}{9}(F - 32)$
   2. $C = \frac{9}{5}(F - 32)$
   3. $C = \frac{5}{9}F - 32$
   4. $C = \frac{9}{5}F + 32$

6. Solve for $b$ in the equation $A = \frac{1}{2}h(a+b)$

   1. $b = \frac{2A}{h} - a$
   2. $b = \frac{A}{2h} - a$
   3. $b = 2A - h - a$
   4. $b = \frac{2A - a}{h}$

7. Solve for $t$ in the equation $d = vt + \frac{1}{2}at^2$, assuming $a=0$.

   1. $t = \frac{d}{v}$
   2. $t = dv$
   3. $t = d - v$
   4. $t = \frac{v}{d}$