Literal Equations and Formula Worksheet

Literal Equations and Formula Worksheet
  • Page 1
 1.  
Use the properties of equality to solve the equation 5a - 2 = 3.
a.
5
b.
5
c.
1
d.
6


Solution:

5a - 2 = 3

5a = 3 + 2 = 5
[Add 2 to both sides of the equation.]

a = 5 / 5 = 1
[Divide throughout by 5.]


Correct answer : (3)
 2.  
Solve the equation 5(12x + 15) = 6x + 19 using the properties of equality.
a.
- 75 56
b.
- 28 27
c.
60
d.
- 10 9


Solution:

5(12x + 15) = 6x + 19

60x + 75 = 6x + 19
[Distributive property.]

54x + 75 = 19
[Subtracting 6x from the two sides of the equation.]

54x = - 56
[Subtracting 75 from the two sides of the equation.]

x = - 28 / 27
[Divide throughout by 54.]

The solution is - 28 / 27.


Correct answer : (2)
 3.  
Solve i9d + 7g = 8 for i.
a.
g + 89d
b.
i8 + 7g
c.
(9d + 7g)
d.
9d(8 - 7g)


Solution:

i9d = 8 - 7g
[Subtracting 7g from the two sides of the equation.]

i = 9d(8 - 7g)
[Multiply throughout by 9d.]


Correct answer : (4)
 4.  
Tell what you would first do to solve the equation 2v + 35 = 3u - 3x for v.
a.
Multiply both sides by 5.
b.
Add 5 to both sides.
c.
Divide both sides by 3x
d.
Multiply both sides by 8


Solution:

2v + 35 = 3u - 3x

To solve the equation, first multiply the two sides by 5
2v + 3 = 5(3u - 3x)


Correct answer : (1)
 5.  
Write the first step to solve the equation: 9c(7j + 8m9 ) = 46 for m. Do not solve the equation.
a.
j + 98m = 46 - 9c
b.
7j + 8m9 = 469c
c.
jm + 99 = 46
d.
9m + 7j = 46c


Solution:

9c(7j + 8m9) = 46

7j + 8m9 = 469c
[Divide throughout by 9c.]


Correct answer : (2)
 6.  
What will be your first step to solve the equation 6r - 7z = 8g2b , for r ?
a.
6r + 7z = 8g2b
b.
2b(6r + 7z) = 8g
c.
r = 8g2b - 7z
d.
6r = 8g2b + 7z


Solution:

6r - 7z = 8g2b

6r = 8g2b + 7z
[Add 7z to both sides of the equation.]


Correct answer : (4)
 7.  
Solve the formula p = 2(l + b) for b.
a.
b = p2 - l
b.
b = p2 + l
c.
b = 2pl
d.
b = 2p


Solution:

p = 2(l + b)

p2 = l + b
[Divide each side of the equation by 2.]

p2 - l = b
[Subtract l from the two sides of the equation.]

b = p2 - l
[Symmetry property.]


Correct answer : (1)
 8.  
Write the first step to solve the equation 5 3(4 + 5h) = 5e for h.
a.
5h = 3 5 + 5e
b.
4 + he = 5
c.
4 - 5h = 3 5 + 5e
d.
4 + 5h = 3 e


Solution:

5 / 3(4 + 5h) = 5e

4 + 5h = 3 e
[Multiply throughout by 3 / 5.]


Correct answer : (4)
 9.  
Solve 6cn + 4j = 5d for n and indicate any restrictions on the values of the variables.
a.
n = 5d + 4j6c, d ≠ 0
b.
n = 5d - 4j6c, c ≠ 0
c.
n = 5d6c - 4j, c ≠ 0
d.
None of the above


Solution:

6cn + 4j = 5d

6cn = 5d - 4j
[Subtracting 4j from the two sides of the equation.]

n = 5d - 4j6c
[Divide throughout by 6c.]

The solution is n = 5d - 4j6c, c ≠ 0
[The solution must exclude values of a variable that make the denominator zero.]


Correct answer : (2)
 10.  
Solve the equation 5h-8b3n = 14e for n, and indicate any restrictions on the values of the variables.
a.
n = 5h-8b42e, e ≠ 0
b.
n = 425h + 8b + e, h + b + e ≠ 0
c.
n = 5h + 8b42
d.
n = 5h + 42be, b ≠ 0, e ≠ 0


Solution:

5h-8b3n = 14e

5h - 8b = 42en
[Multiply throughout by 3n.]

5h - 8b42e = n
[Divide throughout by 42e.]

n = 5n - 8b42e

The solution is n = 5h - 8b42e, e ≠ 0
[The solution must exclude values of a variable that make the denominator zero.]


Correct answer : (1)

*AP and SAT are registered trademarks of the College Board.