Solve I=2/3(7+M)d

$$I = \frac { 2 } { 3 } ( 7 + M ) d$$

Solve for I

$$I=\frac{2d\left(M+7\right)}{3}$$

Solution Steps

Use the distributive property to multiply \frac{2}{3} by 7+M.

$$I=\left(\frac{14}{3}+\frac{2}{3}M\right)d$$

Use the distributive property to multiply \frac{14}{3}+\frac{2}{3}M by d.

$$I=\frac{14}{3}d+\frac{2}{3}Md$$

Solve for M

$$\left\{\begin{matrix}M=\frac{3I}{2d}-7\text{, }&d\neq 0\\M\in \mathrm{R}\text{, }&I=0\text{ and }d=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by 7+M.

$$I=\left(\frac{14}{3}+\frac{2}{3}M\right)d$$

Use the distributive property to multiply \frac{14}{3}+\frac{2}{3}M by d.

$$I=\frac{14}{3}d+\frac{2}{3}Md$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{14}{3}d+\frac{2}{3}Md=I$$

Subtract \frac{14}{3}d from both sides.

$$\frac{2}{3}Md=I-\frac{14}{3}d$$

The equation is in standard form.

$$\frac{2d}{3}M=-\frac{14d}{3}+I$$

Divide both sides by \frac{2}{3}d.

$$\frac{3\times \frac{2d}{3}M}{2d}=\frac{3\left(-\frac{14d}{3}+I\right)}{2d}$$

Dividing by \frac{2}{3}d undoes the multiplication by \frac{2}{3}d.

$$M=\frac{3\left(-\frac{14d}{3}+I\right)}{2d}$$

Divide I-\frac{14d}{3} by \frac{2}{3}d.

$$M=\frac{3I}{2d}-7$$