﻿ Literal Equations and Formula Worksheet | Problems & Solutions

# Literal Equations and Formula Worksheet

Literal Equations and Formula Worksheet
• Page 1
1.
Use the properties of equality to solve the equation 5$a$ - 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.]

2.
Solve the equation 5(12$x$ + 15) = 6$x$ + 19 using the properties of equality.
 a. - $\frac{75}{56}$ b. - $\frac{28}{27}$ c. 60 d. - $\frac{10}{9}$

#### 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.

3.
Solve $\frac{i}{9d}$ + 7$g$ = 8 for $i$.
 a. $g$ + 89$d$ b. $\frac{i}{8}$ + 7$g$ c. (9$d$ + 7$g$) d. 9$d$(8 - 7$g$)

#### Solution:

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

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

4.
Tell what you would first do to solve the equation = 3$u$ - 3$x$ for $v$.
 a. Multiply both sides by 5. b. Add 5 to both sides. c. Divide both sides by 3$x$ 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)

5.
Write the first step to solve the equation: 9$c$(7$j$ + $\frac{\mathrm{8m}}{9}$) = 46 for $m$. Do not solve the equation.
 a. $j$ + $\frac{9}{\mathrm{8m}}$ = 46 - 9$c$ b. 7$j$ + $\frac{8m}{9}$ = $\frac{46}{9c}$ c. $\mathrm{jm}$ + 9$9$ = 46 d. 9$m$ + 7$j$ = 46$c$

#### Solution:

9c(7j + 8m9) = 46

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

6.
What will be your first step to solve the equation 6$r$ - 7$z$ = $\frac{8g}{2b}$ , for $r$ ?
 a. 6$r$ + 7$z$ = $\frac{8g}{2b}$ b. $\mathrm{2b}$(6$r$ + 7$z$) = 8$g$ c. $r$ = $\frac{8g}{2b}$ - 7$z$ d. 6$r$ = $\frac{8g}{2b}$ + 7$z$

#### Solution:

6r - 7z = 8g2b

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

7.
Solve the formula $p$ = 2($l$ + $b$) for $b$.
 a. $b$ = $\frac{p}{2}$ - $l$ b. $b$ = $\frac{p}{2}$ + $l$ c. $b$ = $\frac{2p}{l}$ d. $b$ = $\frac{2}{p}$

#### 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.]

8.
Write the first step to solve the equation $\frac{5}{3}$(4 + 5$h$) = 5$e$ for $h$.
 a. 5$h$ = $\frac{3}{5}$ + 5$e$ b. = 5 c. 4 - 5$h$ = $\frac{3}{5}$ + 5$e$ d. 4 + 5$h$ = 3 $e$

#### Solution:

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

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

9.
Solve 6$\mathrm{cn}$ + 4$j$ = 5$d$ for $n$ and indicate any restrictions on the values of the variables.
 a. $n$ = , $d$ ≠ 0 b. $n$ = , $c$ ≠ 0 c. $n$ = $\frac{5d}{6c}$ - 4$j$, $c$ ≠ 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.]

10.
Solve the equation $\frac{5h-8b}{3n}$ = 14$e$ for $n$, and indicate any restrictions on the values of the variables.
 a. $n$ = $\frac{5h-8b}{42e}$, $e$ ≠ 0 b. $n$ = , $h$ + $b$ + $e$ ≠ 0 c. $n$ = d. $n$ = , $b$ ≠ 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.]