literal equations

by + 2/3 = c for y Subtract 2/3 from each side of the literal equation: by + 2/3 - 2/3 = c - 2/3 Cancel the 2/3 on the left side to get: by = c - 2/3 Divide each side by b to isolate y: by/b = (c - 2/3)/b Cancel the b's on the left side to get: y = (c - 2/3)/b

P/v=nr/t for r Cross multiply to solve this literal equation: Pt = nrv Divide each side of the equation by nv: Pt/nv = nrv/nv Cancel the nv's on the right side, we get: r = Pt/nv

q=c+d/5 for d Subtract c from each side to solve this literal equation: q - c = c - c + d/5 Cancel the c's on the right side, we get d/5 = q - c Multiply each side by 5: 5d/5 = 5(q - c) Cancel the 5's on the left side, we get: d = 5(q - c)

1/a + 1/b = 1/2 for a Subtract 1/b from each side to solve this literal equation: 1/a + 1/b - 1/b = 1/2 - 1/b Cancel the 1/b on the left side, we get: 1/a = 1/2 - 1/b Rewrite the right side, using 2b as a common denominator: 1/a = (b - 2)/2b Cross multiply: a(b - 2) = 2b Divide each side by...

p/q = f/q- f for f Isolate f in this literal equation. Factor out f on the right side: p/q = f(1/q - 1) Rewriting the term in parentheses, we get: p/q = f(1 - q)/q Cross multiply: f = pq/q(1 - q) Cancelling the q/q on the right side, we get: f = p/(1 - q)

ey/n + k = t for y Let's take this literal equation in pieces: Subtract k from each side: ey/n + k - k = t - k Cancel the k's on the left side, we have: ey/n = t - k Now multiply each side by n: ney/n = n(t - k) Cancel the n's on the left side, we have: ey = n(t - k) Divide each side by e...

zy-dm=ky/t for y Isolate terms with y to solve this literal equation. Subtract zy from each side: zy - dm - zy = ky/t - zy Cancel the zy terms on the left side, we get: -dm = ky/t - zy Factor out y: y(k/t - z) = -dm Divide each side by (k/t - z) y = -dm/(k/t - z) (k/t - z) can be rewritten...

r=l^2w/2 for w Solve this literal equation by isolating w. Cross multiply: 2r = l^2w Divide each side by l^2 w = 2r/l^2

z/w=x+z/x+y for z This is a literal equation. Let's isolate z on one side. Subtract z/x from each side. z/w - z/x = x + y Factor our z on the left side: z(1/w - 1/x) = x + y Divide each side by (1/w - 1/x) z = x + y/(1/w - 1/x) To remove reciprocals in the denominator, we rewrite 1/w - 1/x...

p/q=f/q-f for f To solve this literal equation for f, let's factor out f on the right side: p/q=f(1/q-1) Divide each side by (1/q - 1) p/(q(1/q - 1)) = f(1/q-1)/(1/q - 1) Cancelling the (1/q - 1) on the right side, we get: f = p/(1/q - 1) Rewriting this since (1/q -1) = (1 - q)/q since q/q...

m/x = k-6 for m To solve this literal equation, multiply each side by x: x(m/x) = x(k - 6) The x's cancel on the left side, so we get: m = x(k - 6)

If 4x+7=xy-6, then what is the value of x, in terms of y Subtract xy from each side: 4x + 7 - xy = -6 Add 7 to each side: 4x - xy = -6 - 7 4x - xy = -13 Factor out x: x(4 - y) = -13 Divide each side of the equation by (4 - y) x = -13/(4 - y)

x - 5y = 6 for x Add 5y to each side to solve this literal equation for x. x - 5y + 5y = 6 + 5y Cancel the 5y on each side, we get: x = 6 + 5y

V − E + F = 2 for e To solve this literal equation, we want to isolate e. Add E to both sides: V − E + F + E = 2 + E The E's cancel on the left side, so we have: V + F = 2 + E Subtract 2 from each side: V + F - 2 = 2 + E + 2 The 2's cancel on the right side, so we have: E = V + F - 2

n=i*x+y for i This is a literal equation. Subtract y from each side of the equation: n - y = i*x + y - y The y's cancel on the right side, so we have: n - y = ix Divide each side of the equation by x, to isolate i (n - y)/x = ix/x The x's cancel on the right side, so we have: i = (n - y)/x

3k^3 = rt for t This is a literal equation. Let's divide each side of the equation by r, to isolate t: 3k^3/r = rt/r Cancel the r's on the right side, and we get: t = 3k^3/r

acw+cz=y for a Solve this literal equation: Subtract cz from each side: acw + cz - cz = y - cz Cancel the cz on the left side: acw = y - cz Divide each side by cw to isolate a: acw/cw = (y - cz)/cw Cancel cw on the left side: a = (y - cz)/cw

a + b + c = 180 for b We have a literal equation. Subtract (a + c) from each side of the equation to isolate b: a + b + c - (a + c) = 180 - (a + c) The (a + c) cancels on the left side, so we have: b = 180 - (a + c) or, distributing the negative sign: b = 180 - a - c

z=m-x+y, for x This is a literal equation. Let's add subtract (m + y) from each side: z - (m + y) = m - x + y - (m + y) The m + y terms cancel on the right side, so we have: z - m - y = -x Multiply each side by -1 to isolate x: -1(z - m - y) = -(-x) x = m + y - z

j - m/4 = 4k for m Multiply each side by 4: 4j - 4m/4 = 4(4k) Simplify: 4j - m = 16k Add m to each side: 4j - m + m = 16k + m The m's cancel on the left side, so we have: 4j = 16k + m Subtract 16k from each side: 4j - 16k = 16k - 16k + m The 16k cancels on the right side, so we're left...