Pre-Algebra Examples

$\frac{x}{3} + 11 < 31$

Step 1

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

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Step 1.1

Subtract $11$ from both sides of the inequality.

$\frac{x}{3} < 31 - 11$

Step 1.2

Subtract $11$ from $31$ .

$\frac{x}{3} < 20$

Step 2

Multiply both sides by $3$ .

$\frac{x}{3} \cdot 3 < 20 \cdot 3$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $3$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{x}{3} \cdot 3 < 20 \cdot 3$

Step 3.1.1.2

Rewrite the expression.

$x < 20 \cdot 3$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $20$ by $3$ .

$x < 60$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < 60$

Interval Notation:

$(- \infty, 60)$