Pre-Algebra Examples

$3^{x + 1} = 3^{x} + \frac{2}{3}$

Step 1

Factor out $3^{x}$ from the expression.

$3^{x} (3 - 1)$

Step 2

Subtract $3^{x}$ from both sides of the equation.

$3^{x + 1} - 3^{x} = \frac{2}{3}$

Step 3

Subtract $1$ from $3$ .

$3^{x} \cdot 2 = \frac{2}{3}$

Step 4

Move $2$ to the left of $3^{x}$ .

$2 \cdot 3^{x} = \frac{2}{3}$

Step 5

Divide each term in $2 \cdot 3^{x} = \frac{2}{3}$ by $2$ and simplify.

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Step 5.1

Divide each term in $2 \cdot 3^{x} = \frac{2}{3}$ by $2$ .

$\frac{2 \cdot 3^{x}}{2} = \frac{\frac{2}{3}}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{2 \cdot 3^{x}}{2} = \frac{\frac{2}{3}}{2}$

Step 5.2.1.2

Divide $3^{x}$ by $1$ .

$3^{x} = \frac{\frac{2}{3}}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$3^{x} = \frac{2}{3} \cdot \frac{1}{2}$

Step 5.3.2

Cancel the common factor of $2$ .

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Step 5.3.2.1

Cancel the common factor.

$3^{x} = \frac{2}{3} \cdot \frac{1}{2}$

Step 5.3.2.2

Rewrite the expression.

$3^{x} = \frac{1}{3}$

Step 6

Raise $3$ to the power of $1$ .

$3^{x} = \frac{1}{3^{1}}$

Step 7

Move $3^{1}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$3^{x} = 3^{- 1}$

Step 8

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = - 1$