Algebra Examples

$4^{3 x - 1} = 8^{x + 1}$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$2^{2 (3 x - 1)} = 2^{3 (x + 1)}$

Step 2

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

$2 (3 x - 1) = 3 (x + 1)$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (3 x - 1)$ .

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Step 3.1.1

Rewrite.

$0 + 0 + 2 (3 x - 1) = 3 (x + 1)$

Step 3.1.2

Simplify by adding zeros.

$2 (3 x - 1) = 3 (x + 1)$

Step 3.1.3

Apply the distributive property.

$2 (3 x) + 2 \cdot - 1 = 3 (x + 1)$

Step 3.1.4

Multiply.

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Step 3.1.4.1

Multiply $3$ by $2$ .

$6 x + 2 \cdot - 1 = 3 (x + 1)$

Step 3.1.4.2

Multiply $2$ by $- 1$ .

$6 x - 2 = 3 (x + 1)$

Step 3.2

Simplify $3 (x + 1)$ .

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Step 3.2.1

Apply the distributive property.

$6 x - 2 = 3 x + 3 \cdot 1$

Step 3.2.2

Multiply $3$ by $1$ .

$6 x - 2 = 3 x + 3$

Step 3.3

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

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Step 3.3.1

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

$6 x - 2 - 3 x = 3$

Step 3.3.2

Subtract $3 x$ from $6 x$ .

$3 x - 2 = 3$

Step 3.4

Move all terms not containing $x$ to the right side of the equation.

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Step 3.4.1

Add $2$ to both sides of the equation.

$3 x = 3 + 2$

Step 3.4.2

Add $3$ and $2$ .

$3 x = 5$

Step 3.5

Divide each term in $3 x = 5$ by $3$ and simplify.

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Step 3.5.1

Divide each term in $3 x = 5$ by $3$ .

$\frac{3 x}{3} = \frac{5}{3}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $3$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{5}{3}$

Step 3.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5}{3}$

Decimal Form:

$x = 1.\overline{6}$

Mixed Number Form:

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