Algebra Examples

$2^{3 x + 4} < 2^{2 x + 8}$

Step 1

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

$2^{3 x + 4} < 2^{2 x + 8}$

Step 2

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

$3 x + 4 < 2 x + 8$

Step 3

Solve for $x$ .

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Step 3.1

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

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Step 3.1.1

Subtract $2 x$ from both sides of the inequality.

$3 x + 4 - 2 x < 8$

Step 3.1.2

Subtract $2 x$ from $3 x$ .

$x + 4 < 8$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the inequality.

$x < 8 - 4$

Step 3.2.2

Subtract $4$ from $8$ .

$x < 4$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 4$

Interval Notation:

$(- \infty, 4)$

Step 5