literal equations | Page 2 | MathCelebrity Forum

literal equations

1. x/y + 9 = n for x

x/y + 9 = n for x Subtract 9 from each side to isolate the x term: x/y + 9 - 9 = n - 9 Cancel the 9's on the left side and we get: x/y = n - 9 Because we have a fraction on the left side, we can cross multiply the denominator y by n - 9 x = y(n - 9)
2. d - f^3 = 4a for a

d - f^3 = 4a for a Solve this literal equation for a: Divide each side of the equation by 4: (d - f^3)/4 = 4a/4 Cancel the 4's on the right side, and rewrite with our variable to solve for on the left side: a = (d - f^3)/4
3. p = i^2r for r

p = i^2r for r Divide each side of the equation by i^2 to isolate r: p/i^2 = i^2/ri^2 Cancel the i^2 on the right side and we get: r = p/i^2
4. b/3d - h = 343 for b

b/3d - h = 343 for b A literal equation means we solve for one variable in terms of another variable or variables Add h to each side to isolate the b term: b/3d - h + h = 343 + h Cancel the h's on the left side, we get: b/3d = 343 + h Cross multiply: b = 3d(343 + h)
5. ab/d + c = e for d

ab/d + c = e for d I know this is a literal equation because we are asked to solve for a variable in terms of another variable Subtract c from each side to isolate the d term: ab/d + c - c = e - c Cancel the c's on the left side and we get: ab/d = e - c Cross multiply: ab = d(e - c) Divide...
6. 15y + 13/c = m for y

15y + 13/c = m for y Subtract 13/c from each side to isolate the y term: 15y + 13/c - 13/c = m - 13/c Cancel the 13/c on the left side and we get 15y = m - 13/c Now, divide each side by 15 to isolate y: 15y/15 = (m - 13/c)/15 Cancel the 15 on the left side, and we get: y = (m - 13/c)/15
7. a / dc = b for a

a / dc = b for a Cross multiply: a = bcd
8. x/y + 9 = n for y

x/y + 9 = n for y First, subtract 9 from each side to isolate the y term: x/y + 9 - 9 = n - 9 Cancel the 9's on the left side, and we get: x/y = n - 9 Cross multiply: x = y(n - 9) Divide each side by (n - 9): x/(n - 9) = y(n - 9)/(n - 9) Cancel the (n - 9) on the right side, and we get: y =...
9. a = v^2/r for r

a = v^2/r for r Start by cross multiplying to get r out of the denominator: ar = v^2 Divide each side of the equation by a to isolate r: ar/a = v^2/a Cancel the a's on the left side, and we get: r = v^2/a
10. f - g = 1/4b for b

f - g = 1/4b for b Multiply each side of the equation by 4 to remove the 1/4 and isolate b: 4(f - g) = 4/4b 4/4 = 1, so we have: b = 4(f - g) the key to this problem was multiplying by the reciprocal of the constant
11. Solve a= (a + b + c + d)/4 for c

Solve a= (a + b + c + d)/4 for c Cross multiply: 4a = a + b + c + d Subtract a + b+ d from each side to isolate c: 4a - a - b - d = a + b + c + d - a - b - d Canceling the a, b, and d from the right side, we get: c = 3a - b - d
12. x/y = z - 8 for x

x/y = z - 8 for x We start by seeing that x is isolated. To remove y from the left side, we multiply each side of the equation by y: xy/y = y(z - 8) Cancelling y on the left side, we get our answer of: x = y(z - 8)
13. n = b + d^2a for a

n = b + d^2a for a Let's start by isolating the one term with the a variable. Subtract b from each side: n - b = b - b + d^2a Cancel the b terms on the right side and we get: n - b = d^2a With the a term isolated, let's divide each side of the equation by d^2: (n - b)/d^2 = d^2a/d^2 Cancel...
14. x + 8y/4 = 9y for x

x + 8y/4 = 9y for x Step 1: Isolate x by subtracting 8y/4 from each side: x + 8y/4 - 8y/4 = 9y - 8y/4 Cancel 8y/4 on the left side: x = 9y - 8y/4
15. pr=xf/y for r

pr=xf/y for r So for this literal equation, we divide each side of the equation by p to isolate r. pr/p = xf/yp Cancel the p's on the left side and we get: r = xf/yp
16. s=w-10e/m for w

s=w-10e/m for w Add 10e/m to each side to isolate w: s + 10e/m = w - 10e/m + 10e/m Cancel the 10e/m on the right side, and we get: w = s + 10e/m
17. x/y = z - 8 for x

x/y = z - 8 for x Multiply each side by y to isolate x: y*(x/y) = y(z - 8) The y's cancel out on the left side, so we have: x = y(z - 8)
18. s=u^2t for t

s=u^2t for t Divide each side by u^2 to isolate t: u^2t/u^2 = s/u^2 Cancel the u^2 on the left side, we get: t = s/u^2
19. x/3 - g = a for x

x/3 - g = a for x Add g to each side so we can isolate the x term: x/3 - g + g = a + g Cancel the g terms on the left side and we get: x/3 = a + g Multiply each side by 3 to isolate x: 3(x/3) = 3(a + g) Cancelling the 3's on the left side, we get: x = 3(a + g)
20. 2m - n/3 = 5m for n

2m - n/3 = 5m for n Subtract 2m from each side of the equation: 2m-n/3 - 2m = 5m - 2m -n/3 = 3m Multiply each side of the equation by -3 to isolate n: -3 * -n/3 = -3 * 3m n = -9m