Finite Math Examples

$- (2 (x - 1) - 7) \leq 9 x - (3 - x)$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$9 x - (3 - x) \geq - (2 (x - 1) - 7)$

Step 2

Simplify $9 x - (3 - x)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$9 x - 1 \cdot 3 - - x \geq - (2 (x - 1) - 7)$

Step 2.1.2

Multiply $- 1$ by $3$ .

$9 x - 3 - - x \geq - (2 (x - 1) - 7)$

Step 2.1.3

Multiply $- - x$ .

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Step 2.1.3.1

Multiply $- 1$ by $- 1$ .

$9 x - 3 + 1 x \geq - (2 (x - 1) - 7)$

Step 2.1.3.2

Multiply $x$ by $1$ .

$9 x - 3 + x \geq - (2 (x - 1) - 7)$

Step 2.2

Add $9 x$ and $x$ .

$10 x - 3 \geq - (2 (x - 1) - 7)$

Step 3

Simplify $- (2 (x - 1) - 7)$ .

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Step 3.1

Simplify each term.

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Step 3.1.1

Apply the distributive property.

$10 x - 3 \geq - (2 x + 2 \cdot - 1 - 7)$

Step 3.1.2

Multiply $2$ by $- 1$ .

$10 x - 3 \geq - (2 x - 2 - 7)$

Step 3.2

Simplify by multiplying through.

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Step 3.2.1

Subtract $7$ from $- 2$ .

$10 x - 3 \geq - (2 x - 9)$

Step 3.2.2

Apply the distributive property.

$10 x - 3 \geq - (2 x) - - 9$

Step 3.2.3

Multiply.

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Step 3.2.3.1

Multiply $2$ by $- 1$ .

$10 x - 3 \geq - 2 x - - 9$

Step 3.2.3.2

Multiply $- 1$ by $- 9$ .

$10 x - 3 \geq - 2 x + 9$

Step 4

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

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Step 4.1

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

$10 x - 3 + 2 x \geq 9$

Step 4.2

Add $10 x$ and $2 x$ .

$12 x - 3 \geq 9$

Step 5

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

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Step 5.1

Add $3$ to both sides of the inequality.

$12 x \geq 9 + 3$

Step 5.2

Add $9$ and $3$ .

$12 x \geq 12$

Step 6

Divide each term in $12 x \geq 12$ by $12$ and simplify.

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Step 6.1

Divide each term in $12 x \geq 12$ by $12$ .

$\frac{12 x}{12} \geq \frac{12}{12}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $12$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{12 x}{12} \geq \frac{12}{12}$

Step 6.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{12}{12}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $12$ by $12$ .

$x \geq 1$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$x \geq 1$

Interval Notation:

$[1, \infty)$