Algebra Examples

$4^{x + 1} - 32 = 0$

Step 1

Add $32$ to both sides of the equation.

$4^{x + 1} = 32$

Step 2

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

$2^{2 (x + 1)} = 2^{5}$

Step 3

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

$2 (x + 1) = 5$

Step 4

Solve for $x$ .

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Step 4.1

Divide each term in $2 (x + 1) = 5$ by $2$ and simplify.

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Step 4.1.1

Divide each term in $2 (x + 1) = 5$ by $2$ .

$\frac{2 (x + 1)}{2} = \frac{5}{2}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $2$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{2 (x + 1)}{2} = \frac{5}{2}$

Step 4.1.2.1.2

Divide $x + 1$ by $1$ .

$x + 1 = \frac{5}{2}$

Step 4.2

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

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Step 4.2.1

Subtract $1$ from both sides of the equation.

$x = \frac{5}{2} - 1$

Step 4.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = \frac{5}{2} - 1 \cdot \frac{2}{2}$

Step 4.2.3

Combine $- 1$ and $\frac{2}{2}$ .

$x = \frac{5}{2} + \frac{- 1 \cdot 2}{2}$

Step 4.2.4

Combine the numerators over the common denominator.

$x = \frac{5 - 1 \cdot 2}{2}$

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 1$ by $2$ .

$x = \frac{5 - 2}{2}$

Step 4.2.5.2

Subtract $2$ from $5$ .

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

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