Mathematics: Solve the following equation for x (linear equation):

Solve the following equation for x (linear equation):

satwikap3304

16.03.2022

$\displaystyle x=\frac{a+b}{c}$

Step-by-step explanation:

Equations

Solve the equation:

$\displaystyle \frac{b-cx}{a}+\frac{a-cx}{b}+2=0$

Subtracting 2:

$\displaystyle \frac{b-cx}{a}+\frac{a-cx}{b}=-2$

Multiply by ab to eliminate denominators:

$\displaystyle ab\frac{b-cx}{a}+ab\frac{a-cx}{b}=-2ab$

Simplifying:

b(b-cx)+a(a-cx)=-2ab

Operating:

b^2-bcx+a^2-acx=-2ab

Subtracting b^2+a^2

-bcx-acx=-2ab-b^2-a^2

Multiplying by -1:

bcx+acx=2ab+b^2+a^2

Factoring:

c(b+a)x=2ab-b^2+a^2

The right side of the equation is the square of a+b:

c(b+a)x=(a+b)^2

Simplifying (for a ≠ -b):

cx=(a+b)

Dividing by c:

$\boxed{\displaystyle x=\frac{a+b}{c}}$

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jrbdbdj

14.10.2022

The slope of c is a/b.

The equation for the slope of a line is rise/run. a is the rise and b is the run.

Since c is increasing, which you can visualize if you imagine this triangle on Cartesian plane, the slope is positive.

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