Let's solve each of these
literal equations step by step. A literal equation is an equation that involves multiple variables, and we're solving for one specific variable in terms of the others.
---
1. Solve for $ b $:
$$
a + \frac{b}{c} = d
$$
Step 1: Subtract $ a $ from both sides:
$$
\frac{b}{c} = d - a
$$
Step 2: Multiply both sides by $ c $ to isolate $ b $:
$$
b = c(d - a)
$$
✔ Answer: $ \boxed{b = c(d - a)} $
---
2. Isolate the variable $ x $:
$$
3 - x + k = 12
$$
Step 1: Combine constants on the left:
$$
(3 + k) - x = 12
$$
Step 2: Subtract $ (3 + k) $ from both sides:
$$
- x = 12 - (3 + k) = 12 - 3 - k = 9 - k
$$
Step 3: Multiply both sides by $ -1 $:
$$
x = - (9 - k) = k - 9
$$
✔ Answer: $ \boxed{x = k - 9} $
---
3. Solve for $ y $:
$$
\frac{1}{2}(2y - 6n) = 5n
$$
Step 1: Distribute $ \frac{1}{2} $:
$$
\frac{1}{2} \cdot 2y - \frac{1}{2} \cdot 6n = 5n \Rightarrow y - 3n = 5n
$$
Step 2: Add $ 3n $ to both sides:
$$
y = 5n + 3n = 8n
$$
✔ Answer: $ \boxed{y = 8n} $
---
4. Solve for $ w $:
$$
w + 2 = e - 4
$$
Step 1: Subtract 2 from both sides:
$$
w = e - 4 - 2 = e - 6
$$
✔ Answer: $ \boxed{w = e - 6} $
---
5. Find the expression for $ v $:
$$
2(v - 8) = n + y
$$
Step 1: Divide both sides by 2:
$$
v - 8 = \frac{n + y}{2}
$$
Step 2: Add 8 to both sides:
$$
v = \frac{n + y}{2} + 8
$$
✔ Answer: $ \boxed{v = \frac{n + y}{2} + 8} $
---
6. Isolate $ r $:
$$
rs - 5 = t
$$
Step 1: Add 5 to both sides:
$$
rs = t + 5
$$
Step 2: Divide both sides by $ s $:
$$
r = \frac{t + 5}{s}
$$
✔ Answer: $ \boxed{r = \frac{t + 5}{s}} $
---
7. Solve for $ a $:
$$
t - ga = u
$$
Step 1: Subtract $ t $ from both sides:
$$
- ga = u - t
$$
Step 2: Divide both sides by $ -g $:
$$
a = \frac{u - t}{-g} = \frac{t - u}{g}
$$
✔ Answer: $ \boxed{a = \frac{t - u}{g}} $
---
8. Solve for $ b $:
$$
\frac{b - 5}{c} = k
$$
Step 1: Multiply both sides by $ c $:
$$
b - 5 = kc
$$
Step 2: Add 5 to both sides:
$$
b = kc + 5
$$
✔ Answer: $ \boxed{b = kc + 5} $
---
✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 | $ b = c(d - a) $ |
| 2 | $ x = k - 9 $ |
| 3 | $ y = 8n $ |
| 4 | $ w = e - 6 $ |
| 5 | $ v = \frac{n + y}{2} + 8 $ |
| 6 | $ r = \frac{t + 5}{s} $ |
| 7 | $ a = \frac{t - u}{g} $ |
| 8 | $ b = kc + 5 $ |
Let me know if you'd like these written out neatly or formatted for printing!
Parent Tip: Review the logic above to help your child master the concept of literal equation worksheet.
