Algebra Examples

$M = 2 P + 3 Q$

Step 1

Solve the equation for $P$ .

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Step 1.1

Rewrite the equation as $2 P + 3 Q = M$ .

$2 P + 3 Q = M$

Step 1.2

Subtract $3 Q$ from both sides of the equation.

$2 P = M - 3 Q$

Step 1.3

Divide each term in $2 P = M - 3 Q$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 P = M - 3 Q$ by $2$ .

$\frac{2 P}{2} = \frac{M}{2} + \frac{- 3 Q}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 P}{2} = \frac{M}{2} + \frac{- 3 Q}{2}$

Step 1.3.2.1.2

Divide $P$ by $1$ .

$P = \frac{M}{2} + \frac{- 3 Q}{2}$

$P = \frac{M}{2} + \frac{- 3 Q}{2}$

$P = \frac{M}{2} + \frac{- 3 Q}{2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$P = \frac{M}{2} - \frac{3 Q}{2}$

$P = \frac{M}{2} - \frac{3 Q}{2}$

$P = \frac{M}{2} - \frac{3 Q}{2}$

$P = \frac{M}{2} - \frac{3 Q}{2}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $\frac{2 P + 3 Q}{2} - \frac{3 Q}{2}$ .

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Step 2.1.1

Combine the numerators over the common denominator.

$P = \frac{2 P + 3 Q - 3 Q}{2}$

Step 2.1.2

Combine the opposite terms in $2 P + 3 Q - 3 Q$ .

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Step 2.1.2.1

Subtract $3 Q$ from $3 Q$ .

$P = \frac{2 P + 0}{2}$

Step 2.1.2.2

Add $2 P$ and $0$ .

$P = \frac{2 P}{2}$

$P = \frac{2 P}{2}$

Step 2.1.3

Cancel the common factor of $2$ .

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Step 2.1.3.1

Cancel the common factor.

$P = \frac{2 P}{2}$

Step 2.1.3.2

Divide $P$ by $1$ .

$P = P$

$P = P$

$P = P$

$P = P$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$