Solve 8-0.2dt/1+t=1.75dθ

$$\frac { 8 - 0.2 d t } { 1 + t } = 1.75 d \theta$$

Solve for d

$$d=\frac{160}{35t\theta +4t+35\theta }$$

$$\left(\theta =-\frac{4}{35}\text{ or }t\neq -\frac{35\theta }{35\theta +4}\right)\text{ and }t\neq -1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by t+1.

$$8-0.2dt=1.75d\theta \left(t+1\right)$$

Use the distributive property to multiply 1.75d\theta by t+1.

$$8-0.2dt=1.75d\theta t+1.75d\theta$$

Subtract 1.75d\theta t from both sides.

$$8-0.2dt-1.75d\theta t=1.75d\theta$$

Subtract 1.75d\theta from both sides.

$$8-0.2dt-1.75d\theta t-1.75d\theta =0$$

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

$$-0.2dt-1.75d\theta t-1.75d\theta =-8$$

Combine all terms containing d.

$$\left(-0.2t-1.75\theta t-1.75\theta \right)d=-8$$

The equation is in standard form.

$$\left(-\frac{7t\theta }{4}-\frac{t}{5}-\frac{7\theta }{4}\right)d=-8$$

Divide both sides by -0.2t-1.75\theta t-1.75\theta .

$$\frac{\left(-\frac{7t\theta }{4}-\frac{t}{5}-\frac{7\theta }{4}\right)d}{-\frac{7t\theta }{4}-\frac{t}{5}-\frac{7\theta }{4}}=-\frac{8}{-\frac{7t\theta }{4}-\frac{t}{5}-\frac{7\theta }{4}}$$

Dividing by -0.2t-1.75\theta t-1.75\theta undoes the multiplication by -0.2t-1.75\theta t-1.75\theta .

$$d=-\frac{8}{-\frac{7t\theta }{4}-\frac{t}{5}-\frac{7\theta }{4}}$$

Divide -8 by -0.2t-1.75\theta t-1.75\theta .

$$d=\frac{8}{\frac{7t\theta }{4}+\frac{t}{5}+\frac{7\theta }{4}}$$

Solve for t

$$\left\{\begin{matrix}\\t\neq -1\text{, }&\text{unconditionally}\\t=-\frac{5\left(7d\theta -32\right)}{d\left(35\theta +4\right)}\text{, }&d\neq -40\text{ and }\theta \neq -\frac{4}{35}\text{ and }d\neq 0\end{matrix}\right.$$

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.

$$8-0.2dt=1.75d\theta \left(t+1\right)$$

Use the distributive property to multiply 1.75d\theta by t+1.

$$8-0.2dt=1.75d\theta t+1.75d\theta$$

Subtract 1.75d\theta t from both sides.

$$8-0.2dt-1.75d\theta t=1.75d\theta$$

Subtract 8 from both sides.

$$-0.2dt-1.75d\theta t=1.75d\theta -8$$

Combine all terms containing t.

$$\left(-0.2d-1.75d\theta \right)t=1.75d\theta -8$$

The equation is in standard form.

$$\left(-\frac{7d\theta }{4}-\frac{d}{5}\right)t=\frac{7d\theta }{4}-8$$

Divide both sides by -0.2d-1.75d\theta .

$$\frac{\left(-\frac{7d\theta }{4}-\frac{d}{5}\right)t}{-\frac{7d\theta }{4}-\frac{d}{5}}=\frac{\frac{7d\theta }{4}-8}{-\frac{7d\theta }{4}-\frac{d}{5}}$$

Dividing by -0.2d-1.75d\theta undoes the multiplication by -0.2d-1.75d\theta .

$$t=\frac{\frac{7d\theta }{4}-8}{-\frac{7d\theta }{4}-\frac{d}{5}}$$

Divide \frac{7d\theta }{4}-8 by -0.2d-1.75d\theta .

$$t=\frac{7d\theta -32}{-4d\left(\frac{7\theta }{4}+0.2\right)}$$

Variable t cannot be equal to -1.

$$t=\frac{7d\theta -32}{-4d\left(\frac{7\theta }{4}+0.2\right)}\text{, }t\neq -1$$