Finite Math Examples

${(\frac{1}{2})}^{3 x - 1} < {(\frac{1}{2})}^{2 x + 1}$

Step 1

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

${(\frac{1}{2})}^{3 x - 1} < {(\frac{1}{2})}^{2 x + 1}$

Step 2

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

$3 x - 1 < 2 x + 1$

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.

$3 x - 1 - 2 x < 1$

Step 3.1.2

Subtract $2 x$ from $3 x$ .

$x - 1 < 1$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the inequality.

$x < 1 + 1$

Step 3.2.2

Add $1$ and $1$ .

$x < 2$

Step 4

The solution consists of all of the true intervals.

$x > 2$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x > 2$

Interval Notation:

$(2, \infty)$

Step 6