Algebra Examples

$3 (x + 6) - 2 (x + 2) \geq 10$

Step 1

Simplify $3 (x + 6) - 2 (x + 2)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$3 x + 3 \cdot 6 - 2 (x + 2) \geq 10$

Step 1.1.2

Multiply $3$ by $6$ .

$3 x + 18 - 2 (x + 2) \geq 10$

Step 1.1.3

Apply the distributive property.

$3 x + 18 - 2 x - 2 \cdot 2 \geq 10$

Step 1.1.4

Multiply $- 2$ by $2$ .

$3 x + 18 - 2 x - 4 \geq 10$

$3 x + 18 - 2 x - 4 \geq 10$

Step 1.2

Simplify by adding terms.

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Step 1.2.1

Subtract $2 x$ from $3 x$ .

$x + 18 - 4 \geq 10$

Step 1.2.2

Subtract $4$ from $18$ .

$x + 14 \geq 10$

$x + 14 \geq 10$

$x + 14 \geq 10$

Step 2

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

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Step 2.1

Subtract $14$ from both sides of the inequality.

$x \geq 10 - 14$

Step 2.2

Subtract $14$ from $10$ .

$x \geq - 4$

$x \geq - 4$

Step 3

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 4$

Interval Notation:

$[- 4, \infty)$

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