Algebra Examples

$\frac{5}{6} x - 10 \leq 0$ $3 x \leq 1 \frac{1}{3}$

Step 1

Solve $\frac{5}{6} x - 10 \leq 0$ for $x$ .

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Step 1.1

Combine $\frac{5}{6}$ and $x$ .

$\frac{5 x}{6} - 10 \leq 0$

Step 1.2

Add $10$ to both sides of the inequality.

$\frac{5 x}{6} \leq 10$

Step 1.3

Multiply both sides by $6$ .

$\frac{5 x}{6} \cdot 6 \leq 10 \cdot 6$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $6$ .

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Step 1.4.1.1.1

Cancel the common factor.

$\frac{5 x}{6} \cdot 6 \leq 10 \cdot 6$

Step 1.4.1.1.2

Rewrite the expression.

$5 x \leq 10 \cdot 6$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Multiply $10$ by $6$ .

$5 x \leq 60$

Step 1.5

Divide each term in $5 x \leq 60$ by $5$ and simplify.

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Step 1.5.1

Divide each term in $5 x \leq 60$ by $5$ .

$\frac{5 x}{5} \leq \frac{60}{5}$

Step 1.5.2

Simplify the left side.

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Step 1.5.2.1

Cancel the common factor of $5$ .

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Step 1.5.2.1.1

Cancel the common factor.

$\frac{5 x}{5} \leq \frac{60}{5}$

Step 1.5.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{60}{5}$

Step 1.5.3

Simplify the right side.

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Step 1.5.3.1

Divide $60$ by $5$ .

$x \leq 12$

Step 2

Solve $3 x \leq 1 \frac{1}{3}$ for $x$ .

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Step 2.1

Simplify the right side.

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Step 2.1.1

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$3 x \leq 1 + \frac{1}{3}$

Step 2.1.1.2

Add $1$ and $\frac{1}{3}$ .

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Step 2.1.1.2.1

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

$3 x \leq \frac{3}{3} + \frac{1}{3}$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$3 x \leq \frac{3 + 1}{3}$

Step 2.1.1.2.3

Add $3$ and $1$ .

$3 x \leq \frac{4}{3}$

Step 2.2

Divide each term in $3 x \leq \frac{4}{3}$ by $3$ and simplify.

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Step 2.2.1

Divide each term in $3 x \leq \frac{4}{3}$ by $3$ .

$\frac{3 x}{3} \leq \frac{\frac{4}{3}}{3}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $3$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{\frac{4}{3}}{3}$

Step 2.2.2.1.2

Divide $x$ by $1$ .

$x \leq \frac{\frac{4}{3}}{3}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x \leq \frac{4}{3} \cdot \frac{1}{3}$

Step 2.2.3.2

Multiply $\frac{4}{3} \cdot \frac{1}{3}$ .

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Step 2.2.3.2.1

Multiply $\frac{4}{3}$ by $\frac{1}{3}$ .

$x \leq \frac{4}{3 \cdot 3}$

Step 2.2.3.2.2

Multiply $3$ by $3$ .

$x \leq \frac{4}{9}$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \leq \frac{4}{9}$

Interval Notation:

$(- \infty, \frac{4}{9}]$

Step 4