Algebra Examples

$3 x - \frac{5}{6} \geq \frac{- 2 x}{3}$

Step 1

Multiply both sides by $3$ .

$(3 x - \frac{5}{6}) \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(3 x - \frac{5}{6}) \cdot 3$ .

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Step 2.1.1.1

Apply the distributive property.

$3 x \cdot 3 - \frac{5}{6} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Step 2.1.1.2

Multiply $3$ by $3$ .

$9 x - \frac{5}{6} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Step 2.1.1.3

Cancel the common factor of $3$ .

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Step 2.1.1.3.1

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$9 x + \frac{- 5}{6} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Step 2.1.1.3.2

Factor $3$ out of $6$ .

$9 x + \frac{- 5}{3 (2)} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Step 2.1.1.3.3

Cancel the common factor.

$9 x + \frac{- 5}{3 \cdot 2} \cdot 3 \geq \frac{- 2 x}{3} \cdot 3$

Step 2.1.1.3.4

Rewrite the expression.

$9 x + \frac{- 5}{2} \geq \frac{- 2 x}{3} \cdot 3$

Step 2.1.1.4

Move the negative in front of the fraction.

$9 x - \frac{5}{2} \geq \frac{- 2 x}{3} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$9 x - \frac{5}{2} \geq \frac{- 2 x}{3} \cdot 3$

Step 2.2.1.2

Rewrite the expression.

$9 x - \frac{5}{2} \geq - 2 x$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the inequality.

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Step 3.1.1

Add $2 x$ to both sides of the inequality.

$9 x - \frac{5}{2} + 2 x \geq 0$

Step 3.1.2

Add $9 x$ and $2 x$ .

$11 x - \frac{5}{2} \geq 0$

Step 3.2

Add $\frac{5}{2}$ to both sides of the inequality.

$11 x \geq \frac{5}{2}$

Step 3.3

Divide each term in $11 x \geq \frac{5}{2}$ by $11$ and simplify.

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Step 3.3.1

Divide each term in $11 x \geq \frac{5}{2}$ by $11$ .

$\frac{11 x}{11} \geq \frac{\frac{5}{2}}{11}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $11$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{11 x}{11} \geq \frac{\frac{5}{2}}{11}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{\frac{5}{2}}{11}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x \geq \frac{5}{2} \cdot \frac{1}{11}$

Step 3.3.3.2

Multiply $\frac{5}{2} \cdot \frac{1}{11}$ .

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Step 3.3.3.2.1

Multiply $\frac{5}{2}$ by $\frac{1}{11}$ .

$x \geq \frac{5}{2 \cdot 11}$

Step 3.3.3.2.2

Multiply $2$ by $11$ .

$x \geq \frac{5}{22}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq \frac{5}{22}$

Interval Notation:

$[\frac{5}{22}, \infty)$