Algebra Examples

$\frac{2}{3} + \frac{x}{3} > 1$

Step 1

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

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Step 1.1

Subtract $\frac{2}{3}$ from both sides of the inequality.

$\frac{x}{3} > 1 - \frac{2}{3}$

Step 1.2

Write $1$ as a fraction with a common denominator.

$\frac{x}{3} > \frac{3}{3} - \frac{2}{3}$

Step 1.3

Combine the numerators over the common denominator.

$\frac{x}{3} > \frac{3 - 2}{3}$

Step 1.4

Subtract $2$ from $3$ .

$\frac{x}{3} > \frac{1}{3}$

Step 2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x > 1$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x > 1$

Interval Notation:

$(1, \infty)$