Algebra Examples

$3^{3 x + 6} = 27^{x + 2}$

Step 1

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

$3^{3 x + 6} = 3^{3 (x + 2)}$

Step 2

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

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

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Simplify $3 (x + 2)$ .

Tap for more steps...

Step 3.1.1

Rewrite.

$3 x + 6 = 0 + 0 + 3 (x + 2)$

Step 3.1.2

Simplify by adding zeros.

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

Step 3.1.3

Apply the distributive property.

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

Step 3.1.4

Multiply $3$ by $2$ .

$3 x + 6 = 3 x + 6$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$3 x + 6 - 3 x = 6$

Step 3.2.2

Combine the opposite terms in $3 x + 6 - 3 x$ .

Tap for more steps...

Step 3.2.2.1

Subtract $3 x$ from $3 x$ .

$0 + 6 = 6$

Step 3.2.2.2

Add $0$ and $6$ .

$6 = 6$

Step 3.3

Since $6 = 6$ , the equation will always be true.

Always true

Step 4

The result can be shown in multiple forms.

Always true

Interval Notation:

$(- \infty, \infty)$