Question

1. $x = b + \frac{m}{a}$, for $a$
2. $g = x - n + y$, for $x$
3. $g = b - ca$, for $a$
4. $g = ca - b$, for $a$
5. $3x + 4 = xg$, for $x$
6. $g = \frac{1 + 2a}{a}$, for $a$
7. $g = \frac{x - c}{x}$, for $x$
8. $xm = x + z$, for $x$
9. $u + ka = ba$, for $a$
10. $u = kx + yx$, for $x$
11. $u = 3b - 2a + 2$, for $a$
12. $z = 9a - 9 - 3b$, for $a$
13. $g = 4ca - 3ba$, for $a$
14. $-3a - 3 = -2n + 3p$, for $a$
15. $4x = -4r + 2d$, for $x$
16. $u = \frac{-2a - 3}{ka}$, for $a$

Explanation:

15) Step1: Isolate the fraction term

$z - b = \frac{m}{a}$

15) Step2: Cross-multiply to solve for $a$

$a(z - b) = m$

15) Step3: Divide to isolate $a$

$a = \frac{m}{z - b}$

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16) Step1: Isolate $x$ term

$g - z - y = x$

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17) Step1: Rearrange to isolate $a$ term

$g - b = -ca$

17) Step2: Divide to solve for $a$

$a = \frac{b - g}{c}$

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18) Step1: Isolate $a$ term

$g + b = ca$

18) Step2: Divide to solve for $a$

$a = \frac{g + b}{c}$

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19) Step1: Isolate $x$ terms

$2x - xg = -4$

19) Step2: Factor out $x$

$x(2 - g) = -4$

19) Step3: Divide to solve for $x$

$x = \frac{-4}{2 - g} = \frac{4}{g - 2}$

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20) Step1: Multiply both sides by $a$

$ga = 1 + 2a$

20) Step2: Isolate $a$ terms

$ga - 2a = 1$

20) Step3: Factor out $a$

$a(g - 2) = 1$

20) Step4: Divide to solve for $a$

$a = \frac{1}{g - 2}$

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21) Step1: Multiply both sides by $x$

$gx = x - c$

21) Step2: Isolate $x$ terms

$gx - x = -c$

21) Step3: Factor out $x$

$x(g - 1) = -c$

21) Step4: Divide to solve for $x$

$x = \frac{-c}{g - 1} = \frac{c}{1 - g}$

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22) Step1: Isolate $x$ terms

$xm - x = z$

22) Step2: Factor out $x$

$x(m - 1) = z$

22) Step3: Divide to solve for $x$

$x = \frac{z}{m - 1}$

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23) Step1: Isolate $a$ terms

$ka - ba = -u$

23) Step2: Factor out $a$

$a(k - b) = -u$

23) Step3: Divide to solve for $a$

$a = \frac{-u}{k - b} = \frac{u}{b - k}$

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24) Step1: Factor out $x$

$u = x(k + y)$

24) Step2: Divide to solve for $x$

$x = \frac{u}{k + y}$

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25) Step1: Isolate $a$ term

$u - 3b - 2 = -2a$

25) Step2: Divide to solve for $a$

$a = \frac{3b + 2 - u}{2}$

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26) Step1: Isolate $a$ term

$z + 9 + 3b = 9a$

26) Step2: Divide to solve for $a$

$a = \frac{z + 3b + 9}{9}$

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27) Step1: Factor out $a$

$g = a(4c - 3b)$

27) Step2: Divide to solve for $a$

$a = \frac{g}{4c - 3b}$

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28) Step1: Isolate $a$ term

$-3a = -2n + 3p + 3$

28) Step2: Divide to solve for $a$

$a = \frac{2n - 3p - 3}{3}$

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29) Step1: Divide by 4 to solve for $x$

$x = \frac{-4r + 2d}{4}$

29) Step2: Simplify the fraction

$x = \frac{-2r + d}{2}$

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30) Step1: Multiply both sides by $ka$

$uka = -2a - 3$

30) Step2: Isolate $a$ terms

$uka + 2a = -3$

30) Step3: Factor out $a$

$a(uk + 2) = -3$

30) Step4: Divide to solve for $a$

$a = \frac{-3}{uk + 2}$

Answer:

1. $a = \frac{m}{z - b}$
2. $x = g - z - y$
3. $a = \frac{b - g}{c}$
4. $a = \frac{g + b}{c}$
5. $x = \frac{4}{g - 2}$
6. $a = \frac{1}{g - 2}$
7. $x = \frac{c}{1 - g}$
8. $x = \frac{z}{m - 1}$
9. $a = \frac{u}{b - k}$
10. $x = \frac{u}{k + y}$
11. $a = \frac{3b + 2 - u}{2}$
12. $a = \frac{z + 3b + 9}{9}$
13. $a = \frac{g}{4c - 3b}$
14. $a = \frac{2n - 3p - 3}{3}$
15. $x = \frac{-2r + d}{2}$
16. $a = \frac{-3}{uk + 2}$