Algebra Examples

$3 x - 7 \geq 2 (x - 7)$

Step 1

Simplify $2 (x - 7)$ .

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Step 1.1

Rewrite.

$3 x - 7 \geq 0 + 0 + 2 (x - 7)$

Step 1.2

Simplify by adding zeros.

$3 x - 7 \geq 2 (x - 7)$

Step 1.3

Apply the distributive property.

$3 x - 7 \geq 2 x + 2 \cdot - 7$

Step 1.4

Multiply $2$ by $- 7$ .

$3 x - 7 \geq 2 x - 14$

Step 2

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

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Step 2.1

Subtract $2 x$ from both sides of the inequality.

$3 x - 7 - 2 x \geq - 14$

Step 2.2

Subtract $2 x$ from $3 x$ .

$x - 7 \geq - 14$

Step 3

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

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Step 3.1

Add $7$ to both sides of the inequality.

$x \geq - 14 + 7$

Step 3.2

Add $- 14$ and $7$ .

$x \geq - 7$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \geq - 7$

Interval Notation:

$[- 7, \infty)$