Algebra Examples

x - 3 > 3 (x - 1)

$x - 3 > 3 (x - 1)$

Step 1

Simplify

3 (x - 1)

$3 (x - 1)$ .

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Step 1.1

Rewrite.

x - 3 > 0 + 0 + 3 (x - 1)

$x - 3 > 0 + 0 + 3 (x - 1)$

Step 1.2

Simplify by adding zeros.

x - 3 > 3 (x - 1)

$x - 3 > 3 (x - 1)$

Step 1.3

Apply the distributive property.

x - 3 > 3 x + 3 \cdot - 1

$x - 3 > 3 x + 3 \cdot - 1$

Step 1.4

Multiply

3

$3$ by

- 1

$- 1$ .

x - 3 > 3 x - 3

$x - 3 > 3 x - 3$

x - 3 > 3 x - 3

$x - 3 > 3 x - 3$

Step 2

Move all terms containing

x

$x$ to the left side of the inequality.

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Step 2.1

Subtract

3 x

$3 x$ from both sides of the inequality.

x - 3 - 3 x > - 3

$x - 3 - 3 x > - 3$

Step 2.2

Subtract

3 x

$3 x$ from

x

$x$ .

- 2 x - 3 > - 3

$- 2 x - 3 > - 3$

- 2 x - 3 > - 3

$- 2 x - 3 > - 3$

Step 3

Move all terms not containing

x

$x$ to the right side of the inequality.

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Step 3.1

Add

3

$3$ to both sides of the inequality.

- 2 x > - 3 + 3

$- 2 x > - 3 + 3$

Step 3.2

Add

- 3

$- 3$ and

3

$3$ .

- 2 x > 0

$- 2 x > 0$

- 2 x > 0

$- 2 x > 0$

Step 4

Divide each term in

- 2 x > 0

$- 2 x > 0$ by

- 2

$- 2$ and simplify.

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Step 4.1

Divide each term in

- 2 x > 0

$- 2 x > 0$ by

- 2

$- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

\frac{- 2 x}{- 2} < \frac{0}{- 2}

$\frac{- 2 x}{- 2} < \frac{0}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 4.2.1.1

Cancel the common factor.

\frac{- 2 x}{- 2} < \frac{0}{- 2}

$\frac{- 2 x}{- 2} < \frac{0}{- 2}$

Step 4.2.1.2

Divide

x

$x$ by

1

$1$ .

x < \frac{0}{- 2}

$x < \frac{0}{- 2}$

x < \frac{0}{- 2}

$x < \frac{0}{- 2}$

x < \frac{0}{- 2}

$x < \frac{0}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide

0

$0$ by

- 2

$- 2$ .

x < 0

$x < 0$

x < 0

$x < 0$

x < 0

$x < 0$

Step 5

The result can be shown in multiple forms.

Inequality Form:

x < 0

$x < 0$

Interval Notation:

(- \infty, 0)

$(- \infty, 0)$