Practice worksheet for solving literal equations in two steps, with problems to solve for variables y, t, b, p, n, and v.

You're working on solving literal equations for a specified variable — this means rearranging the equation so that the desired variable is isolated on one side. These are “two-step” problems, meaning you typically need to perform two inverse operations (like adding/subtracting and then multiplying/dividing) to isolate the variable.

Let’s solve each equation step-by-step.

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🔹 Left Column

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1. Solve for y:  3y – x = 5

We want to get `y` by itself.

Step 1: Add `x` to both sides to eliminate `-x`:

> 3y = 5 + x

Step 2: Divide both sides by 3:

> y = (5 + x)/3

✔ Answer: y = (x + 5)/3

*(Note: We write it as (x + 5)/3 for standard form, but (5 + x)/3 is also correct.)*

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2. Solve for b:  w = 2b – 4

We want to isolate `b`.

Step 1: Add 4 to both sides:

> w + 4 = 2b

Step 2: Divide both sides by 2:

> b = (w + 4)/2

✔ Answer: b = (w + 4)/2

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3. Solve for p:  m = –2p + 3

Isolate `p`.

Step 1: Subtract 3 from both sides:

> m – 3 = –2p

Step 2: Divide both sides by –2:

> p = (m – 3)/(–2)

We can simplify by writing the negative in front:

> p = –(m – 3)/2
> or p = (3 – m)/2

✔ Answer: p = (3 – m)/2

*(This is cleaner than leaving the negative denominator.)*

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4. Solve for n:  2w = 2n + 3

Isolate `n`.

Step 1: Subtract 3 from both sides:

> 2w – 3 = 2n

Step 2: Divide both sides by 2:

> n = (2w – 3)/2

✔ Answer: n = (2w – 3)/2

*(Can also be written as n = w – 3/2, but unless asked to split, leave as single fraction.)*

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🔹 Right Column

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5. Solve for t:  g = 4t – 5

Isolate `t`.

Step 1: Add 5 to both sides:

> g + 5 = 4t

Step 2: Divide both sides by 4:

> t = (g + 5)/4

✔ Answer: t = (g + 5)/4

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6. Solve for b:  k = –2b + 1

Isolate `b`.

Step 1: Subtract 1 from both sides:

> k – 1 = –2b

Step 2: Divide both sides by –2:

> b = (k – 1)/(–2)
> or b = –(k – 1)/2
> or b = (1 – k)/2

✔ Answer: b = (1 – k)/2

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7. Solve for v:  r = (5v)/2

Isolate `v`.

Step 1: Multiply both sides by 2 to eliminate the denominator:

> 2r = 5v

Step 2: Divide both sides by 5:

> v = (2r)/5

✔ Answer: v = (2r)/5

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8. Solve for p:  2p + 1 = h

Isolate `p`.

Step 1: Subtract 1 from both sides:

> 2p = h – 1

Step 2: Divide both sides by 2:

> p = (h – 1)/2

✔ Answer: p = (h – 1)/2

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## ✔ Final Answers Summary:

| Equation | Solved for Variable | Answer |
|----------|---------------------|--------|
| 3y – x = 5 | y | y = (x + 5)/3 |
| w = 2b – 4 | b | b = (w + 4)/2 |
| m = –2p + 3 | p | p = (3 – m)/2 |
| 2w = 2n + 3 | n | n = (2w – 3)/2 |
| g = 4t – 5 | t | t = (g + 5)/4 |
| k = –2b + 1 | b | b = (1 – k)/2 |
| r = (5v)/2 | v | v = (2r)/5 |
| 2p + 1 = h | p | p = (h – 1)/2 |

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💡 Tip: When solving literal equations, always:
- Identify the target variable.
- Use inverse operations to undo what’s being done to it.
- Keep the equation balanced (do the same thing to both sides).
- Simplify the final expression if possible.

Let me know if you’d like to see these solved with diagrams or visual steps!