Question

solve each literal equation for the given value. 1-) A = 4lw + bh for h2-) L = a(1+ct) for c3-) y = x(3-yz) for z4-) r = s-s1t for s15-) y = 12xy+3xz for x6-) x = n/m-k for kShow that when the equation n= (a+b)c is solved for b, the result is b= n-ac/cShow that when L= E/R+K is solved for R, the result is R=E-LK/L

Answer 1

We have the followiing:

1. A = 4lw + bh

solving for h

$\begin{gathered} bh=A-4lw \\ h=\frac{A-4lw}{b} \end{gathered}$

2. L = a(1+ct)

solving for c

$\begin{gathered} L=a+act \\ act=L-a \\ c=\frac{L-a}{at} \end{gathered}$

3. y = x(3-yz)

solving for z

$\begin{gathered} y=3x-xyz \\ xyz=3x-y \\ z=\frac{3x-y}{xy} \end{gathered}$

4. r = s-s1t

solving for s1

$\begin{gathered} s_1t=r-s \\ s_1=\frac{r-2}{t} \end{gathered}$

5. y = 12xy+3xz

solving for x

$\begin{gathered} 12xy+3xz=y \\ x(12y+3z)=y \\ x=\frac{y}{12y+3z} \end{gathered}$

6. x = n/m-k

solving for k

$\begin{gathered} x\cdot(m-k)=n \\ xm-xk=n \\ xk=xm-n \\ k=\frac{xm-n}{x} \end{gathered}$

n= (a+b)c

solving for b

$\begin{gathered} n=ac+bc \\ bc=n-ac \\ b=\frac{n-ac}{c} \end{gathered}$

L= E/R+K

solving for R

$\begin{gathered} L\cdot(R+K)=E \\ LR+LK=E \\ LR=E-LK \\ R=\frac{E-LK}{L} \end{gathered}$