Algebra Examples

$- \frac{1}{3} x + 5 < 3$

Step 1

Combine $x$ and $\frac{1}{3}$ .

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

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the inequality.

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

Step 2.2

Subtract $5$ from $3$ .

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

Step 3

Divide each term in $- \frac{x}{3} < - 2$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- \frac{x}{3} < - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

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

Step 3.2.2

Divide $\frac{x}{3}$ by $1$ .

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

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $- 2$ by $- 1$ .

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

Step 4

Multiply both sides by $3$ .

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

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $3$ .

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Step 5.1.1.1

Cancel the common factor.

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

Step 5.1.1.2

Rewrite the expression.

$x > 2 \cdot 3$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $2$ by $3$ .

$x > 6$

Step 6