Solve 7P(1/2)=8(1/2)^3-k

$$7 P ( \frac { 1 } { 2 } ) = 8 ( \frac { 1 } { 2 } ) ^ { 3 } - k$$

Solve for P

$$P=\frac{2-2k}{7}$$

Steps for Solving Linear Equation

Multiply 7 and \frac{1}{2} to get \frac{7}{2}.

$$\frac{7}{2}P=8\times \left(\frac{1}{2}\right)^{3}-k$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{7}{2}P=8\times \frac{1}{8}-k$$

Multiply 8 and \frac{1}{8} to get 1.

$$\frac{7}{2}P=1-k$$

Divide both sides of the equation by \frac{7}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{7}{2}P}{\frac{7}{2}}=\frac{1-k}{\frac{7}{2}}$$

Dividing by \frac{7}{2} undoes the multiplication by \frac{7}{2}.

$$P=\frac{1-k}{\frac{7}{2}}$$

Divide 1-k by \frac{7}{2} by multiplying 1-k by the reciprocal of \frac{7}{2}.

$$P=\frac{2-2k}{7}$$

Solve for k

$$k=-\frac{7P}{2}+1$$

Steps for Solving Linear Equation

Multiply 7 and \frac{1}{2} to get \frac{7}{2}.

$$\frac{7}{2}P=8\times \left(\frac{1}{2}\right)^{3}-k$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{7}{2}P=8\times \frac{1}{8}-k$$

Multiply 8 and \frac{1}{8} to get 1.

$$\frac{7}{2}P=1-k$$

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

$$1-k=\frac{7}{2}P$$

Subtract 1 from both sides.

$$-k=\frac{7}{2}P-1$$

The equation is in standard form.

$$-k=\frac{7P}{2}-1$$

Divide both sides by -1.

$$\frac{-k}{-1}=\frac{\frac{7P}{2}-1}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k=\frac{\frac{7P}{2}-1}{-1}$$

Divide \frac{7P}{2}-1 by -1.

$$k=-\frac{7P}{2}+1$$