Algebra Examples

$5 > 2 + \frac{x}{3}$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$2 + \frac{x}{3} < 5$

Step 2

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

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Step 2.1

Subtract $2$ from both sides of the inequality.

$\frac{x}{3} < 5 - 2$

Step 2.2

Subtract $2$ from $5$ .

$\frac{x}{3} < 3$

Step 3

Multiply both sides by $3$ .

$\frac{x}{3} \cdot 3 < 3 \cdot 3$

Step 4

Simplify.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

$\frac{x}{3} \cdot 3 < 3 \cdot 3$

Step 4.1.1.2

Rewrite the expression.

$x < 3 \cdot 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $3$ by $3$ .

$x < 9$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x < 9$

Interval Notation:

$(- \infty, 9)$