Algebra Examples

$3^{4 x - 2} = 9^{- (x + 1)}$

Step 1

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

$3^{4 x - 2} = 3^{2 (- (x + 1))}$

Step 2

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

$4 x - 2 = 2 (- (x + 1))$

Step 3

Solve for $x$ .

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Step 3.1

Simplify $2 (- (x + 1))$ .

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Step 3.1.1

Rewrite.

$4 x - 2 = 0 + 0 + 2 (- (x + 1))$

Step 3.1.2

Simplify by adding zeros.

$4 x - 2 = 2 (- (x + 1))$

Step 3.1.3

Apply the distributive property.

$4 x - 2 = 2 (- x - 1 \cdot 1)$

Step 3.1.4

Multiply $- 1$ by $1$ .

$4 x - 2 = 2 (- x - 1)$

Step 3.1.5

Apply the distributive property.

$4 x - 2 = 2 (- x) + 2 \cdot - 1$

Step 3.1.6

Multiply.

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Step 3.1.6.1

Multiply $- 1$ by $2$ .

$4 x - 2 = - 2 x + 2 \cdot - 1$

Step 3.1.6.2

Multiply $2$ by $- 1$ .

$4 x - 2 = - 2 x - 2$

Step 3.2

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

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Step 3.2.1

Add $2 x$ to both sides of the equation.

$4 x - 2 + 2 x = - 2$

Step 3.2.2

Add $4 x$ and $2 x$ .

$6 x - 2 = - 2$

Step 3.3

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

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Step 3.3.1

Add $2$ to both sides of the equation.

$6 x = - 2 + 2$

Step 3.3.2

Add $- 2$ and $2$ .

$6 x = 0$

Step 3.4

Divide each term in $6 x = 0$ by $6$ and simplify.

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Step 3.4.1

Divide each term in $6 x = 0$ by $6$ .

$\frac{6 x}{6} = \frac{0}{6}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $6$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{0}{6}$

Step 3.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{6}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $0$ by $6$ .

$x = 0$