Solve (epsilon + a) * bol = (x*varphi)/(6varphi) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(\epsilon+a)bol=\frac{x\varphi}{6\varphi}$$

Solve for a (complex solution)

$\left\{\begin{matrix}a=\frac{x-6bloϵ}{6blo}\text{, }&l\neq 0\text{ and }o\neq 0\text{ and }b\neq 0\text{ and }\phi \neq 0\\a\in \mathrm{C}\text{, }&\left(l=0\text{ or }o=0\text{ or }b=0\right)\text{ and }x=0\text{ and }\phi \neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $6\phi $.

$$\left(ϵ+a\right)bol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵ+a$ by $b$.

$$\left(ϵb+ab\right)ol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵb+ab$ by $o$.

$$\left(ϵbo+abo\right)l\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbo+abo$ by $l$.

$$\left(ϵbol+abol\right)\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbol+abol$ by $6$.

$$\left(6ϵbol+6abol\right)\phi =x\phi $$

Use the distributive property to multiply $6ϵbol+6abol$ by $\phi $.

$$6ϵbol\phi +6abol\phi =x\phi $$

Subtract $6ϵbol\phi $ from both sides.

$$6abol\phi =x\phi -6ϵbol\phi $$

The equation is in standard form.

$$6blo\phi a=x\phi -6blo\phi ϵ$$

Divide both sides by $6bol\phi $.

$$\frac{6blo\phi a}{6blo\phi }=\frac{\phi \left(x-6bloϵ\right)}{6blo\phi }$$

Dividing by $6bol\phi $ undoes the multiplication by $6bol\phi $.

$$a=\frac{\phi \left(x-6bloϵ\right)}{6blo\phi }$$

Divide $\phi \left(x-6ϵbol\right)$ by $6bol\phi $.

$$a=-ϵ+\frac{x}{6blo}$$

Solve for b (complex solution)

$\left\{\begin{matrix}b=\frac{x}{6lo\left(a+ϵ\right)}\text{, }&ϵ\neq -a\text{ and }l\neq 0\text{ and }o\neq 0\text{ and }\phi \neq 0\\b\in \mathrm{C}\text{, }&\left(ϵ=-a\text{ or }l=0\text{ or }o=0\right)\text{ and }x=0\text{ and }\phi \neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $6\phi $.

$$\left(ϵ+a\right)bol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵ+a$ by $b$.

$$\left(ϵb+ab\right)ol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵb+ab$ by $o$.

$$\left(ϵbo+abo\right)l\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbo+abo$ by $l$.

$$\left(ϵbol+abol\right)\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbol+abol$ by $6$.

$$\left(6ϵbol+6abol\right)\phi =x\phi $$

Use the distributive property to multiply $6ϵbol+6abol$ by $\phi $.

$$6ϵbol\phi +6abol\phi =x\phi $$

Combine all terms containing $b$.

$$\left(6ϵol\phi +6aol\phi \right)b=x\phi $$

The equation is in standard form.

$$\left(6alo\phi +6lo\phi ϵ\right)b=x\phi $$

Divide both sides by $6ϵol\phi +6aol\phi $.

$$\frac{\left(6alo\phi +6lo\phi ϵ\right)b}{6alo\phi +6lo\phi ϵ}=\frac{x\phi }{6alo\phi +6lo\phi ϵ}$$

Dividing by $6ϵol\phi +6aol\phi $ undoes the multiplication by $6ϵol\phi +6aol\phi $.

$$b=\frac{x\phi }{6alo\phi +6lo\phi ϵ}$$

Divide $x\phi $ by $6ϵol\phi +6aol\phi $.

$$b=\frac{x}{6lo\left(a+ϵ\right)}$$

Solve for a

$\left\{\begin{matrix}a=\frac{x-6bloϵ}{6blo}\text{, }&l\neq 0\text{ and }o\neq 0\text{ and }b\neq 0\text{ and }\phi \neq 0\\a\in \mathrm{R}\text{, }&\left(l=0\text{ or }o=0\text{ or }b=0\right)\text{ and }x=0\text{ and }\phi \neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $6\phi $.

$$\left(ϵ+a\right)bol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵ+a$ by $b$.

$$\left(ϵb+ab\right)ol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵb+ab$ by $o$.

$$\left(ϵbo+abo\right)l\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbo+abo$ by $l$.

$$\left(ϵbol+abol\right)\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbol+abol$ by $6$.

$$\left(6ϵbol+6abol\right)\phi =x\phi $$

Use the distributive property to multiply $6ϵbol+6abol$ by $\phi $.

$$6ϵbol\phi +6abol\phi =x\phi $$

Subtract $6ϵbol\phi $ from both sides.

$$6abol\phi =x\phi -6ϵbol\phi $$

The equation is in standard form.

$$6blo\phi a=x\phi -6blo\phi ϵ$$

Divide both sides by $6bol\phi $.

$$\frac{6blo\phi a}{6blo\phi }=\frac{\phi \left(x-6bloϵ\right)}{6blo\phi }$$

Dividing by $6bol\phi $ undoes the multiplication by $6bol\phi $.

$$a=\frac{\phi \left(x-6bloϵ\right)}{6blo\phi }$$

Divide $\phi \left(x-6ϵbol\right)$ by $6bol\phi $.

$$a=-ϵ+\frac{x}{6blo}$$

Solve for b

$\left\{\begin{matrix}b=\frac{x}{6lo\left(a+ϵ\right)}\text{, }&ϵ\neq -a\text{ and }l\neq 0\text{ and }o\neq 0\text{ and }\phi \neq 0\\b\in \mathrm{R}\text{, }&\left(ϵ=-a\text{ or }l=0\text{ or }o=0\right)\text{ and }x=0\text{ and }\phi \neq 0\end{matrix}\right.$

Steps for Solving Linear Equation

Multiply both sides of the equation by $6\phi $.

$$\left(ϵ+a\right)bol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵ+a$ by $b$.

$$\left(ϵb+ab\right)ol\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵb+ab$ by $o$.

$$\left(ϵbo+abo\right)l\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbo+abo$ by $l$.

$$\left(ϵbol+abol\right)\times 6\phi =x\phi $$

Use the distributive property to multiply $ϵbol+abol$ by $6$.

$$\left(6ϵbol+6abol\right)\phi =x\phi $$

Use the distributive property to multiply $6ϵbol+6abol$ by $\phi $.

$$6ϵbol\phi +6abol\phi =x\phi $$

Combine all terms containing $b$.

$$\left(6ϵol\phi +6aol\phi \right)b=x\phi $$

The equation is in standard form.

$$\left(6alo\phi +6lo\phi ϵ\right)b=x\phi $$

Divide both sides by $6ϵol\phi +6aol\phi $.

$$\frac{\left(6alo\phi +6lo\phi ϵ\right)b}{6alo\phi +6lo\phi ϵ}=\frac{x\phi }{6alo\phi +6lo\phi ϵ}$$

Dividing by $6ϵol\phi +6aol\phi $ undoes the multiplication by $6ϵol\phi +6aol\phi $.

$$b=\frac{x\phi }{6alo\phi +6lo\phi ϵ}$$

Divide $x\phi $ by $6ϵol\phi +6aol\phi $.

$$b=\frac{x}{6lo\left(a+ϵ\right)}$$