Algebra Examples

$\frac{6 (x - 3)}{8} \geq 3$

Step 1

Cancel the common factor of $6$ and $8$ .

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Step 1.1

Factor $2$ out of $6 (x - 3)$ .

$\frac{2 (3 (x - 3))}{8} \geq 3$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $8$ .

$\frac{2 (3 (x - 3))}{2 (4)} \geq 3$

Step 1.2.2

Cancel the common factor.

$\frac{2 (3 (x - 3))}{2 \cdot 4} \geq 3$

Step 1.2.3

Rewrite the expression.

$\frac{3 (x - 3)}{4} \geq 3$

$\frac{3 (x - 3)}{4} \geq 3$

$\frac{3 (x - 3)}{4} \geq 3$

Step 2

Multiply both sides by $4$ .

$\frac{3 (x - 3)}{4} \cdot 4 \geq 3 \cdot 4$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{3 (x - 3)}{4} \cdot 4$ .

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Step 3.1.1.1

Cancel the common factor of $4$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{3 (x - 3)}{4} \cdot 4 \geq 3 \cdot 4$

Step 3.1.1.1.2

Rewrite the expression.

$3 (x - 3) \geq 3 \cdot 4$

$3 (x - 3) \geq 3 \cdot 4$

Step 3.1.1.2

Apply the distributive property.

$3 x + 3 \cdot - 3 \geq 3 \cdot 4$

Step 3.1.1.3

Multiply $3$ by $- 3$ .

$3 x - 9 \geq 3 \cdot 4$

$3 x - 9 \geq 3 \cdot 4$

$3 x - 9 \geq 3 \cdot 4$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $3$ by $4$ .

$3 x - 9 \geq 12$

$3 x - 9 \geq 12$

$3 x - 9 \geq 12$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Add $9$ to both sides of the inequality.

$3 x \geq 12 + 9$

Step 4.1.2

Add $12$ and $9$ .

$3 x \geq 21$

$3 x \geq 21$

Step 4.2

Divide each term in $3 x \geq 21$ by $3$ and simplify.

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Step 4.2.1

Divide each term in $3 x \geq 21$ by $3$ .

$\frac{3 x}{3} \geq \frac{21}{3}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $3$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} \geq \frac{21}{3}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{21}{3}$

$x \geq \frac{21}{3}$

$x \geq \frac{21}{3}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $21$ by $3$ .

$x \geq 7$

$x \geq 7$

$x \geq 7$

$x \geq 7$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$x \geq 7$

Interval Notation:

$[7, \infty)$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$