Solve 8-02dt/1+t=175dθ

$$\frac { 8 - 02 d t } { 1 + t } = 175 d \theta$$

Solve for d

$$d=\frac{8}{175t\theta +2t+175\theta }$$

$$\left(\theta =-\frac{2}{175}\text{ or }t\neq -\frac{175\theta }{175\theta +2}\right)\text{ and }t\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t+1.

$$8-2dt=175d\theta \left(t+1\right)$$

Use the distributive property to multiply 175d\theta by t+1.

$$8-2dt=175d\theta t+175d\theta$$

Subtract 175d\theta t from both sides.

$$8-2dt-175d\theta t=175d\theta$$

Subtract 175d\theta from both sides.

$$8-2dt-175d\theta t-175d\theta =0$$

Subtract 8 from both sides. Anything subtracted from zero gives its negation.

$$-2dt-175d\theta t-175d\theta =-8$$

Combine all terms containing d.

$$\left(-2t-175\theta t-175\theta \right)d=-8$$

The equation is in standard form.

$$\left(-175t\theta -2t-175\theta \right)d=-8$$

Divide both sides by -175t\theta -2t-175\theta .

$$\frac{\left(-175t\theta -2t-175\theta \right)d}{-175t\theta -2t-175\theta }=-\frac{8}{-175t\theta -2t-175\theta }$$

Dividing by -175t\theta -2t-175\theta undoes the multiplication by -175t\theta -2t-175\theta .

$$d=-\frac{8}{-175t\theta -2t-175\theta }$$

Divide -8 by -175t\theta -2t-175\theta .

$$d=\frac{8}{175t\theta +2t+175\theta }$$

Solve for t

$$\left\{\begin{matrix}t=\frac{8-175d\theta }{d\left(175\theta +2\right)}\text{, }&d\neq -4\text{ and }\theta \neq -\frac{2}{175}\text{ and }d\neq 0\\t\neq -1\text{, }&\theta =-\frac{2}{175}\text{ and }d=-4\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable t cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by t+1.

$$8-2dt=175d\theta \left(t+1\right)$$

Use the distributive property to multiply 175d\theta by t+1.

$$8-2dt=175d\theta t+175d\theta$$

Subtract 175d\theta t from both sides.

$$8-2dt-175d\theta t=175d\theta$$

Subtract 8 from both sides.

$$-2dt-175d\theta t=175d\theta -8$$

Combine all terms containing t.

$$\left(-2d-175d\theta \right)t=175d\theta -8$$

The equation is in standard form.

$$\left(-175d\theta -2d\right)t=175d\theta -8$$

Divide both sides by -2d-175\theta d.

$$\frac{\left(-175d\theta -2d\right)t}{-175d\theta -2d}=\frac{175d\theta -8}{-175d\theta -2d}$$

Dividing by -2d-175\theta d undoes the multiplication by -2d-175\theta d.

$$t=\frac{175d\theta -8}{-175d\theta -2d}$$

Divide 175d\theta -8 by -2d-175\theta d.

$$t=\frac{175d\theta -8}{-d\left(175\theta +2\right)}$$

Variable t cannot be equal to -1.

$$t=\frac{175d\theta -8}{-d\left(175\theta +2\right)}\text{, }t\neq -1$$