Algebra Examples

$- \frac{2}{3} p + \frac{8}{3} = - 3 p$

Step 1

Simplify each term.

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Step 1.1

Combine $p$ and $\frac{2}{3}$ .

$- \frac{p \cdot 2}{3} + \frac{8}{3} = - 3 p$

Step 1.2

Move $2$ to the left of $p$ .

$- \frac{2 p}{3} + \frac{8}{3} = - 3 p$

Step 2

Move all terms containing $p$ to the left side of the equation.

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Step 2.1

Add $3 p$ to both sides of the equation.

$- \frac{2 p}{3} + \frac{8}{3} + 3 p = 0$

Step 2.2

To write $3 p$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{2 p}{3} + 3 p \cdot \frac{3}{3} + \frac{8}{3} = 0$

Step 2.3

Combine $3 p$ and $\frac{3}{3}$ .

$- \frac{2 p}{3} + \frac{3 p \cdot 3}{3} + \frac{8}{3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{- 2 p + 3 p \cdot 3}{3} + \frac{8}{3} = 0$

Step 2.5

Combine the numerators over the common denominator.

$\frac{- 2 p + 3 p \cdot 3 + 8}{3} = 0$

Step 2.6

Multiply $3$ by $3$ .

$\frac{- 2 p + 9 p + 8}{3} = 0$

Step 2.7

Add $- 2 p$ and $9 p$ .

$\frac{7 p + 8}{3} = 0$

Step 3

Set the numerator equal to zero.

$7 p + 8 = 0$

Step 4

Solve the equation for $p$ .

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Step 4.1

Subtract $8$ from both sides of the equation.

$7 p = - 8$

Step 4.2

Divide each term in $7 p = - 8$ by $7$ and simplify.

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Step 4.2.1

Divide each term in $7 p = - 8$ by $7$ .

$\frac{7 p}{7} = \frac{- 8}{7}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $7$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{7 p}{7} = \frac{- 8}{7}$

Step 4.2.2.1.2

Divide $p$ by $1$ .

$p = \frac{- 8}{7}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Move the negative in front of the fraction.

$p = - \frac{8}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = - \frac{8}{7}$

Decimal Form:

$p = - 1.\overline{142857}$

Mixed Number Form:

$p = - 1 \frac{1}{7}$