Question # 17 Solution
Answer:
[tex]x_{1}= \frac{mx_{2}-y_{2}+y_{1}}{m}[/tex]
Step-by-step Explanation:
The given expression
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
And we have to solve for x₁
So,
Lets solve for x₁.
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Multiply both sides by x₂ - x₁
[tex]m(x_{2}-x_{1})= (x_{2}-x_{1})\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m(x_{2}-x_{1})= (y_{2}-y_{1})[/tex]
[tex]mx_{2}-mx_{1}= (y_{2}-y_{1})[/tex]
[tex]-mx_{1}= y_{2}-y_{1}-mx_{2}[/tex]
Divide both sides by -m
[tex]\frac{-mx_{1}}{-m}= \frac{y_{2}-y_{1}-mx_{2}}{-m}[/tex]
[tex]x_{1}= \frac{mx_{2}-y_{2}+y_{1}}{m}[/tex]
Therefore, [tex]x_{1}= \frac{mx_{2}-y_{2}+y_{1}}{m}[/tex]
Question # 23 Solution
Answer:
[tex]n= \frac{bx}{-b + x}[/tex]
Step-by-step Explanation:
The given expression
[tex]\frac{nx}{b}-x=x[/tex]
And we have to solve for n
So,
Let's solve for n.
[tex]\frac{nx}{b}-x=x[/tex]
Multiply both sides by b.
[tex]-bn + nx = bx[/tex]
Factor out n.
[tex]n(-b + x)= bx[/tex]
Divide both sides by -b + x.
[tex]\frac{n(-b + x)}{-b + x}= \frac{bx}{-b + x}[/tex]
[tex]n= \frac{bx}{-b + x}[/tex]
Therefore, [tex]n= \frac{bx}{-b + x}[/tex]
Keywords: solution, equation
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