Question

Literal equations

1) g = x - c, for x
2) u = k / a, for a
3) g = x + c, for x
4) z = a - m, for a
5) u = a - k, for a
6) ac = dr, for a
7) c / a = dr, for a
8) k / x = w - v, for x
9) m / a = p + n, for a
10) u = b + k - a, for a
11) a - k = b + vw, for a
12) ma = b + n - p, for a
13) am = b (p - n), for a
14) mx = y (p - n ), for x
15) g = (r + d) (x - c), for x

Show your work, please. It is highly appreciated but not required.

Answer 1

The solutions to the given equations are

1) x = g + c

2) $a = \frac{k}{u}$ OR a = k/u

3) x = g - c

4) a = z + m

5) a = u + k

6) $a = \frac{dr}{c}$ Or a = dr/c

7) $a = \frac{c}{dr}$ OR a = c / dr

8) $x = \frac{k}{w-v}$ OR x = k /(w-v)

9) $a =\frac{m}{p+n}$ OR a = m/(p+n)

10) a = b + k - u

11) a = b + k + vw

12) $a = \frac{b+n-p}{m}$ OR a = (b+n-p)/m

13)  $a= \frac{b(p-n)}{m}$ OR a = b(p-n)/m

14) $x = \frac{y(p-n)}{m}$ OR x = y(p-n)/m

15) $x = \frac{g}{(r+d)} +c$

For each of the equations, we will solve for the required variable

1) g = x - c, for x

To solve for x, we will add c to both sides, that is

g +c = x - c + c

g + c = x

∴ x = g + c

2) u = k / a, for a

This can be written as $u = \frac{k}{a}$

To solve for a, we will first multiply both sides by a, that is

$a \times u = \frac{k}{a} \times a$

Then, we get

$au = k$

Now, divide both sides by u

$\frac{au}{u} = \frac{k}{u}$

∴ $a = \frac{k}{u}$ OR a = k/u

3) g = x + c, for x

To solve for x, we will subtract c from both sides

g - c = x + c - c

g - c = x

∴ x = g - c

4) z = a - m, for a

To solve for a, we will add m to both sides

z + m = a - m + m

z + m = a

∴ a = z + m

5)  u = a - k, for a

To solve for a, we will add k to both sides

u + k = a - k + k

u + k = a

∴ a = u + k

6) ac = dr, for a

Here, to solve for a, we will divide both sides by c

$\frac{ac}{c} = \frac{dr}{c}$

∴ $a = \frac{dr}{c}$ Or a = dr/c

7) c / a = dr, for a

This can be written as

$\frac{c}{a} = dr$

To solve for a, we will first multiply both sides by a

$a \times \frac{c}{a} = dr \times a$

$c = dra$

Now, divide both sides by dr

$\frac{c}{dr} = \frac{dra}{dr}$

$\frac{c}{dr} = a$

∴ $a = \frac{c}{dr}$ OR a = c / dr

8)  k / x = w - v, for x

This can be written as

$\frac{k}{x} = w-v$

To solve for x we will first multiply both sides by x

$x\times \frac{k}{x} =x \times (w-v)$

$k =x (w-v)$

Now, divide both sides by (w - v)

$\frac{k}{(w-v)} = \frac{x(w-v)}{(w-v)}$

$\frac{k}{w-v} = x$

∴ $x = \frac{k}{w-v}$ OR x = k /(w-v)

9) m / a = p + n, for a

This can be written as

$\frac{m}{a} = p + n$

To solve for a, we will first multiply both sides by a

$a \times \frac{m}{a} = a \times (p + n)$

$m = a (p + n)$

Now, divide both sides by (p+n)

$\frac{m}{(p+n)} = \frac{a(p+n)}{(p+n)}$

$\frac{m}{p+n} = a$

∴ $a =\frac{m}{p+n}$ OR a = m/(p+n)

10) u = b + k - a, for a

To solve for a, we will subtract (b + k) from both sides

u - (b + k) = b + k - (b + k) - a

u - b - k = b + k - b - k - a

Then,

u - b - k = - a

Now, multiply through by -1

-1 ×(u - b - k) = -1 × -a

-u +b +k = a

Then, we can write that

b + k - u = a

∴ a = b + k - u

11) a - k = b + vw, for a

To solve for a, add k to both sides

a - k + k = b + k + vw

∴ a = b + k + vw

12) ma = b + n - p, for a

To solve for a, divide both sides by m

$\frac{ma}{m} = \frac{b+n-p}{m}$

∴ $a = \frac{b+n-p}{m}$ OR a = (b+n-p)/m

13) am = b (p - n), for a

To solve for a, divide both sides by m, that is

$\frac{am}{m} = \frac{b(p-n)}{m}$

∴ $a= \frac{b(p-n)}{m}$ OR a = b(p-n)/m

14) mx = y (p - n ), for x

To solve for x, divide both sides by m

$\frac{mx}{m} = \frac{y(p-n)}{m}$

∴ $x = \frac{y(p-n)}{m}$ OR x = y(p-n)/m

15) g = (r + d) (x - c), for x

To solve for x,

First, divide both sides by (r + d)

$\frac{g}{(r+d)} = \frac{(r+d)(x-c)}{(r+d)}$

$\frac{g}{(r+d)} = x -c$

Now, add c to both sides

$\frac{g}{(r+d)} + c= x -c+c$

$\frac{g}{(r+d)} + c= x$

∴ $x = \frac{g}{(r+d)} +c$

Hence, the solutions to the given equations are

1) x = g + c

2) $a = \frac{k}{u}$ OR a = k/u

3) x = g - c

4) a = z + m

5) a = u + k

6) $a = \frac{dr}{c}$ Or a = dr/c

7) $a = \frac{c}{dr}$ OR a = c / dr

8) $x = \frac{k}{w-v}$ OR x = k /(w-v)

9) $a =\frac{m}{p+n}$ OR a = m/(p+n)

10) a = b + k - u

11) a = b + k + vw

12) $a = \frac{b+n-p}{m}$ OR a = (b+n-p)/m

13)  $a= \frac{b(p-n)}{m}$ OR a = b(p-n)/m

14) $x = \frac{y(p-n)}{m}$ OR x = y(p-n)/m

15) $x = \frac{g}{(r+d)} +c$

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