Literal Equations

Show your work for each problem.

1.
Which of the following is a literal equation?
1. a)
2. b)
3. c)
4. d)
Answer:
is a literal equation because it contains three different variables: , , and . The other options have only one variable or no variables.
2.
Solve for . Enter your answer as a fraction (e.g., A/b).
Answer: A/b
Starting with , divide both sides by : . The 's cancel on the right, giving .
3.
Solve for .
1. a)
2. b)
3. c)
4. d)
Answer:
Since is multiplied by , divide both sides by : , which gives .
4.
Solve for . Enter your answer as a fraction.
Answer: I/(rt)
To isolate , divide both sides by : . This gives .
5.
Solve for .
Answer: d/r
1. What variable do we want to isolate? t
2. What operation connects to ? multiplication
3. What inverse operation should we use? division
4. Divide both sides by . What is ? d/r
6.
Solve for .
1. a)
2. b)
3. c)
4. d)
Answer:
Step 1: Subtract : . Step 2: Divide by : .
7.
Solve for . Enter your answer as a fraction.
Answer: d/v
Step 1: Multiply both sides by : . Step 2: Divide both sides by : .
8.
Solve for .
Answer: (P-2l)/2
1. What term should we subtract first to isolate the term? 2l
2. After subtracting , what equation do we have? P - 2l = 2w
3. What do we divide both sides by to isolate ? 2
4. What is ? (P-2l)/2
9.
Solve for .
1. a)
2. b)
3. c)
4. d)
Answer:
Divide both sides by : . The 's cancel: .
10.
Solve for .
Answer: C/(2*pi)
1. What is multiplied by? 2*pi
2. What operation should we use to isolate ? division
3. Divide both sides by . What is ? C/(2*pi)
11.
Solve for . Enter your answer as a fraction.
Answer: (y-b)/m
Step 1: Subtract : . Step 2: Divide by : .
12.
Solve for .
1. a)
2. b)
3. c)
4. d)
Answer:
Step 1: Subtract 32: . Step 2: Multiply by : .
13.
Solve for .
Answer: 2A/b
1. To eliminate , multiply both sides by what? 2
2. After multiplying by 2, what equation do we have? 2A = bh
3. Now divide both sides by . What is ? 2A/b
14.
Solve for . Enter your answer as a fraction.
Answer: V/(lh)
Since is multiplied by both and , divide both sides by : .
15.
Solve for .
Answer: (c-ax)/b
1. What term should we subtract to isolate the term? ax
2. After subtracting , what do we have? by = c - ax
3. What do we divide by to get alone? b
4. What is ? (c-ax)/b
16.
Solve for .
1. a)
2. b)
3. c)
4. d)
Answer:
Step 1: Multiply by : . Step 2: Subtract : .
17.
Solve for (sum of arithmetic sequence formula).
Answer: 2S/n - a
1. First, multiply both sides by 2 to clear the fraction. What do we get? 2S = n(a + l)
2. Divide both sides by . What do we get? 2S/n = a + l
3. Subtract from both sides. What is ? 2S/n - a