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=(A-4lw)/(b) \end{gathered}`

2. L = a(1+ct)

solving for c

`\begin{gathered} L=a+act \\ act=L-a \\ c=(L-a)/(at) \end{gathered}`

3. y = x(3-yz)

solving for z

`\begin{gathered} y=3x-xyz \\ xyz=3x-y \\ z=(3x-y)/(xy) \end{gathered}`

4. r = s-s1t

solving for s1

`\begin{gathered} s_1t=r-s \\ s_1=(r-2)/(t) \end{gathered}`

5. y = 12xy+3xz

solving for x

`\begin{gathered} 12xy+3xz=y \\ x(12y+3z)=y \\ x=(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=(xm-n)/(x) \end{gathered}`

n= (a+b)c

solving for b

`\begin{gathered} n=ac+bc \\ bc=n-ac \\ b=(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=(E-LK)/(L) \end{gathered}`